CBSE Class 12 Maths

Matrices

Each concept is a short lesson, then questions until you get three right.

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6 concepts, a short lesson each

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Types of matrices

Order is rows × columns; square, diagonal, scalar, identity, triangular, zero; singular when the determinant is 0

Types of matricesOrder is rows × columns; square, diagonal, scalar, identity, triangular, zero; singular when the determinant is 0Start
Adding matrices and scalar multiplesSame order only; add entry by entry; a scalar multiplies every entryStart
Multiplying matrices $(AB)_{ij}$ = row $i$ of $A$ times column $j$ of $B$ ; needs columns of $A$ = rows of $B$ Start
Properties of matrix multiplication $AB \ne BA$ in general; $AB = O$ without $A$ or $B$ being $O$ ; $A^2$ means $A \cdot A$ Start
The transposeRows become columns; $(A + B)^T = A^T + B^T$ and $(AB)^T = B^TA^T$ , order reversedStart
Symmetric and skew-symmetric matrices $A^T = A$ or $A^T = -A$ (diagonal all 0); every square matrix is $\frac{A + A^T}{2} + \frac{A - A^T}{2}$ Start

Practise Matrices

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answers Past board questionsAsked from this chapter, with solutions