CLASS XII
MATHEMATICS
HOT PRACTICE TEST
Chapter 3 – Matrices
Higher Order Thinking Practice Test • 25 Marks
Matrix Representation
Section A – 6 × 1 = 6
1. If A is a square matrix, when is A called symmetric?
2. Find the order of a matrix containing 12 elements arranged in 3 rows.
3. If A is a 2 × 2 identity matrix, find A².
4. Can a rectangular matrix have an inverse?
5. If A = Aᵀ, what type of matrix is A?
6. State whether matrix multiplication is commutative in general.
Section B – 3 × 2 = 6
1. Given A=[[1,2],[3,4]], calculate 2A−Aᵀ.
2. Show using an example that AB may exist while BA does not.
3. Express a 2 × 2 matrix as the sum of a symmetric and a skew-symmetric matrix.
Section C – 3 × 3 = 9
1. Find X if [[1,2],[0,1]]X=[[3,4],[2,3]].
2. If A²−5A+6I=0, determine A⁻¹ in terms of A.
3. Using elementary operations, find the inverse of [[2,1],[3,2]].
Section D – 1 × 4 = 4
1. Let A be a square matrix satisfying A²−4A+3I=0. Derive an expression for A⁻¹ and explain why A must be invertible.