Matrices Questions with Solutions

25 questions7 easy11 medium7 hard

A matrix is a rectangular arrangement of numbers in rows and columns. This topic covers types of matrices (square, diagonal, scalar, identity, symmetric and skew-symmetric), matrix operations (addition, scalar multiplication and matrix multiplication), the transpose, determinants and their properties, minors and cofactors, the adjoint, and the inverse of a matrix. It also covers solving systems of linear equations using the inverse method and elementary row and column transformations. Remember that matrix multiplication is not commutative, so AB need not equal BA, and that the inverse exists only when the determinant is not zero. Useful results include |AB| = |A||B|, (AB)^-1 = B^-1 A^-1, and |kA| = k^n |A| for a matrix of order n. These properties solve many questions without heavy calculation. Practise the matrices questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
If A and B are square matrices such that $B = - A^{- 1} B A$ , then $(A + B)^{2}$ is
A. $O$ (the zero matrix)B. $A^{2} + B^{2}$ C. $A^{2} + 2 A B + B^{2}$ D. $A + B$
easyAsked in NIMCET 2023View solution ›
Q2.
If $A$ is a $3 \times 3$ matrix with $d e t (A) = 3$ , then $d e t (a d j A)$ is:
A. 3B. 9C. 27D. 6
easyAsked in NIMCET 2009View solution ›
Q3.
Let $A = (a_{ij})$ and $B = (b_{ij})$ be two square matrices of order n and det(A) denotes the determinant of A. Then, which of the following is not correct?
A. If A is a diagonal matrix, then $d e t (A) = a_{11} a_{22} \dots a_{nn}$ B. $d e t (A B) = d e t (A) d e t (B)$ C. $d e t (c A) = c d e t (A)$ D. $d e t (A) = d e t (A^{T})$ , where $A^{T}$ denotes the transpose of the matrix A
easyAsked in NIMCET 2020View solution ›
Q4.
If $F (θ) = [cos θ - s in θ 0 s in θ cos θ 0001]$ , then $F (θ) F (α)$ is equal to
A. $F (θ α)$ B. $F (\frac{θ}{α})$ C. $F (θ + α)$ D. $F (θ - α)$
easyAsked in NIMCET 2021View solution ›
Q5.
If the matrix $[- 1321 k - 3145]$ has an inverse matrix, then the value of k is:
A. k is any real numberB. $k \neq = - 4$ C. $k = - 4$ D. $k \neq = 4$
easyAsked in NIMCET 2014View solution ›
Q6.
A matrix $M_{r}$ is defined as $M_{r} = [r r - 1 r - 1 r]$ , $r \in N$ . Then the value of $d e t (M_{1}) + d e t (M_{2}) + \dots + d e t (M_{2015})$ is
A. $2014^{2}$ B. $2013^{2}$ C. 2014D. $2015^{2}$
easyAsked in NIMCET 2015View solution ›
Q7.
If $A = [0500]$ and $f (x) = 1 + x + x^{2} + \dots + x^{16}$ , then $f (A) =$
A. $0$ B. $[1501]$ C. $[1500]$ D. $[0511]$
easyAsked in NIMCET 2018View solution ›