The Matrices Class 12 Formula Sheet will include all important formulas and derivations of Chapter 3 in a single PDF. You can either take a printout and fix it in front of your study table or read in an offline mode during exam time. This page covers definitions, solved examples, exam-weightage and common mistakes, with every formula following the CBSE marking scheme used in recent board papers.
- CBSE Weightage: 5 to 7 marks (one short answer plus one MCQ or assertion-reason item).
- JEE Main Weightage: 3 to 5% of the Maths section (1 to 2 questions per paper).
- CUET (UG) Weightage: 1 to 2 MCQs in nearly every shift.
This Formula Sheet is curated by Class 12 Maths experts at Collegedunia, mapped to the 2026-27 NCERT edition, and refined against the last five years of CBSE Board and JEE Main papers.
All Matrices Formulas for Class 12 Maths in One learn Table
The this Class 12 page address this in the same order as the NCERT textbook.
The table below catalogues every formula, identity, and special-matrix definition from Class 12 Maths Chapter 3, mapped to the exact NCERT section where it is introduced. Each row has surfaced in a CBSE or JEE Main question in the last five years, so anchor your revision around it.
| Concept | Formula / Rule | NCERT Section | Common Use |
|---|---|---|---|
| Order of a matrix | Am × n has m rows, n columns | 3.2 | Compatibility check |
| Number of elements | m × n | 3.2 | 1-mark MCQ |
| Number of matrices of order m × n with entries from a set of size k | km · n | 3.2 (extension) | JEE counting |
| Equality of matrices | A = B aij = bij for all i, j and same order | 3.3 | Solving entry equations |
| Addition | (A + B)ij = aij + bij , same order | 3.4.1 | Operation MCQ |
| Scalar multiplication | (kA)ij = k · aij | 3.4.2 | Solving kA = B |
| Subtraction | (A - B)ij = aij - bij , same order | 3.4.3 | Operation MCQ |
| Multiplication compatibility | Am × n · Bn × p = (AB)m × p | 3.4.4 | Order matching |
| Matrix multiplication entry | (AB)ij = k=1n aik bkj | 3.4.4 | 3-mark CBSE compute |
| Non-commutativity | In general, AB ≠ BA | 3.4.4 | Assertion-reason |
| Associativity | (AB)C = A(BC) | 3.4.4 | Multi-step proof |
| Distributivity | A(B + C) = AB + AC | 3.4.4 | Identity proofs |
| Identity matrix | AIn = In A = A , where A is n × n | 3.4.4 | Standard recall |
| Zero product property failure | AB = O does NOT imply A = O or B = O | 3.4.4 | Assertion-reason MCQ |
| Transpose | (AT)ij = aji | 3.5 | Definition recall |
| Transpose of sum | (A + B)T = AT + BT | 3.5 | 2-mark CBSE |
| Transpose of scalar product | (kA)T = k AT | 3.5 | 1-mark MCQ |
| Transpose of product (reversal law) | (AB)T = BT AT | 3.5 | JEE Main |
| Double transpose | (AT)T = A | 3.5 | Definition recall |
| Symmetric matrix | AT = A , so aij = aji | 3.6 | 3-mark proof |
| Skew-symmetric matrix | AT = -A , so aij = -aji and aii = 0 | 3.6 | 3-mark proof |
| Symmetric part of A | P = 12(A + AT) | 3.6 | Decomposition (Step 1) |
| Skew-symmetric part of A | Q = 12(A - AT) | 3.6 | Decomposition (Step 2) |
| Unique decomposition | Every square matrix A = P + Q (symmetric + skew-symmetric) | 3.6 | 5-mark CBSE |
| Number of independent entries (symmetric, n × n) | n(n+1)2 | 3.6 (extension) | JEE counting |
| Number of independent entries (skew-symmetric, n × n) | n(n-1)2 | 3.6 (extension) | JEE counting |
| Row matrix | Order 1 × n | 3.2 | Definition |
| Column matrix | Order m × 1 | 3.2 | Definition |
| Square matrix | Order n × n | 3.2 | Definition |
| Diagonal matrix | aij = 0 for all i ≠ j | 3.2 | Definition |
| Scalar matrix | Diagonal with all diagonal entries equal | 3.2 | Definition |
| Identity matrix entries | In = [ij] , where ij = 1 if i = j , else 0 | 3.2 | Definition |
| Zero matrix | All entries are 0 | 3.2 | Definition |
| Trace of a square matrix | tr(A) = i=1n aii | 3.4 (extension) | JEE Main |
| Trace properties | tr(A + B) = tr(A) + tr(B), tr(AB) = tr(BA) | 3.4 (extension) | JEE Main |
| Power of a matrix | Ak = A · A · … · A (k times); valid only for square A | 3.4 (extension) | Cayley-style problems |
Around 8 of these 36 rules cover the entire 5 to 7 mark CBSE budget for the the resource every year.
Matrices Video Walkthrough
Source: Magnet Brains on YouTube
Types of Matrices: Compact Definition Strip
The the PDF address this in the same order as the NCERT textbook.
Class 12 Maths Chapter 3 catalogues eight standard matrix types, and CBSE 1-mark questions routinely ask students to identify one from a sample. The strip below lists the order signature for each type so you can classify any given matrix in seconds.
| Type | Defining Rule | Example Order |
|---|---|---|
| Row matrix | Single row | 1 × n |
| Column matrix | Single column | m × 1 |
| Square matrix | Rows = columns | n × n |
| Diagonal matrix | Square, off-diagonal entries all 0 | n × n |
| Scalar matrix | Diagonal with equal diagonal entries | n × n |
| Identity matrix In | Scalar with diagonal entry 1 | n × n |
| Zero matrix O | All entries 0 | m × n |
| Symmetric / Skew-symmetric | AT = A or AT = -A | n × n |
Top 5 Most-Asked Topics from Matrices in Class 12 Board Exams
The ranking below shows which sub-topics of Matrices have driven the most marks in CBSE Class 12 Maths papers from 2025 back to 2021. Anchor your last revision pass on these five.
- Symmetric and skew-symmetric decomposition of a 3x3 matrix (5 marks, almost every year).
- Matrix multiplication and order matching (2 to 3 marks, every year).
- Transpose reversal law verification (AB)T = BT AT (2 marks, 4 of last 5 years).
- Matrix equality and entry equations (2 marks, recurring).
- Special-matrix type identification (1 mark assertion-reason or MCQ).
Full year-wise PYQ map: Matrices Class 12 Maths NCERT Solutions
Other Resources from Collegedunia
NCERT Formula Sheet for Class 12 Maths: All Chapters
Use the table below to jump to the Formula Sheet of any other Class 12 Maths chapter. Each link opens the same learn-table format you have on this page.
| Chapter | Resource |
|---|---|
| Chapter 3 | Matrices Formula Sheet |
| Chapter 1 | Relations and Functions Formula Sheet |
| Chapter 2 | Inverse Trigonometric Functions Formula Sheet |
| Chapter 4 | Determinants Formula Sheet |
| Chapter 5 | Continuity and Differentiability Formula Sheet |
| Chapter 6 | Application of Derivatives Formula Sheet |
| Chapter 7 | Integrals Formula Sheet |
| Chapter 8 | Application of Integrals Formula Sheet |
| Chapter 9 | Differential Equations Formula Sheet |
| Chapter 10 | Vector Algebra Formula Sheet |
| Chapter 11 | Three Dimensional Geometry Formula Sheet |
| Chapter 12 | Linear Programming Formula Sheet |
| Chapter 13 | Probability Formula Sheet |
this chapter: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Matrices formula sheet made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Matrices Formulas for Class 12 - Frequently Asked Questions
Ques. Where can I download these notes for free?
Ans. You can download the Class 12 Maths Chapter 3 Matrices Formula Sheet PDF directly from the download card on this page. Both the Normal and HD versions are free and cover every formula listed in the learn table above, including the symmetric or skew-symmetric decomposition and the JEE Main counting extensions.
Ques. Is the Matrices formula sheet aligned with the 2026-27 NCERT?
Ans. Yes. Every formula matches the current 2026-27 syllabus for Class 12 Maths Chapter 3. Topics dropped from the board syllabus (elementary row operations, inverse via row reduction) are flagged as "extension" rows so board-only students know they can skip them, while JEE aspirants still get the full coverage.
Ques. How many pages is the Class 12 Maths Chapter 3 Matrices Formula Sheet PDF?
Ans. The Matrices Formula Sheet PDF runs 7 pages and packs every operation rule, transpose identity, symmetric or skew-symmetric definition, and counting extension from Chapter 3, plus the quick-fact card grid and the compatibility-rule decision tree.
Ques. What is the formula for the transpose of a product of matrices in Class 12 Maths?
Ans. The reversal law states (AB)T = BT AT . The transpose of a product equals the product of the individual transposes in the reverse order. The same rule extends to three or more matrices: (ABC)T = CT BT AT .
Ques. How do I express a square matrix as the sum of a symmetric and skew-symmetric matrix?
Ans. Use the decomposition template. Step 1: compute AT. Step 2 (1.5 marks): write the symmetric part P = 12(A + AT) . Step 3 (1.5 marks): write the skew-symmetric part Q = 12(A - AT) . Step 4 (1 mark): verify PT = P and QT = -Q. Step 5 (1 mark): conclude A = P + Q .
Ques. How many independent entries does an n by n symmetric matrix have?
Ans. A symmetric matrix of order n × n has exactly n(n+1)2 independent entries (the diagonal plus one triangle). A skew-symmetric matrix of the same order has only n(n-1)2 independent entries, because the diagonal entries are forced to be zero. For n = 3, this gives 6 and 3 respectively.
Ques. Is matrix multiplication commutative in Class 12 Maths Chapter 3?
Ans. No, matrix multiplication is not commutative in general. For most square matrices A and B, AB ≠ BA . Commutativity only holds in special cases (e.g. when one of the matrices is the identity or a scalar matrix, or when both matrices are diagonal). CBSE assertion-reason MCQs exploit this fact almost every year.
Ques. What is the number of matrices of order 2 by 2 with entries 0 or 1?
Ans. Using the counting formula kmn with k = 2 (two choices per entry) and mn = 4 (four entries), the total is 24 = 16 . This counting question is a recurring 1-mark JEE Main and CUET MCQ; the same logic gives 34 = 81 for entries from 0, 1, 2, and so on.
Comments