Algebra

Matrices & Determinants

Easy

The number of all different possible matrices of order $2 \times 2$ with each entry $-1$ , $0$ or $1$ is :

✅ Correct Option: 2

A $2 \times 2$ matrix has $4$ entries. Each entry can independently take one of $3$ values $(-1, 0, 1)$ . Total number of matrices $= 3^4 = 81$ .

2025: 29 May Shift 2

The inverse of the matrix $\begin{bmatrix} 4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6 \end{bmatrix}$ is

2025: 22 May Shift 1

If A is a skew-symmetric matrix, then which of the following statements is NOT true?

(A) A is singular if order of A is odd

(B) A is non-singular

(D) $A^{2025}$ is a symmetric matrix

(E) all diagonal elements of A are zeros

Choose the correct answer from the options given below:

2022: 25 May Shift 1

If matrix A is of order $2 \times 3$ and B of order $3 \times 2$ , then

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
Matrix A	$\left\vert \text{adj } A \right\vert^2$
(A) $\begin{bmatrix} 3 & 7 \\ 2 & 8 \end{bmatrix}$	(I) $121$
(B) $\begin{bmatrix} 5 & -1 \\ 2 & 4 \end{bmatrix}$	(II) $144$
(C) $\begin{bmatrix} 3 & 6 \\ 5 & 14 \end{bmatrix}$	(III) $484$
(D) $\begin{bmatrix} 7 & 5 \\ 2 & 3 \end{bmatrix}$	(IV) $100$

Choose the correct answer from the options given below:

2026: 14 May Shift 2

If $a,b,c$ are the roots of $x^3+px+q=0$ , then the value of $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is equal to

2026: 15 May Shift 1

If $A = [a_{ij}]_{3\times3}, a_{ij} = 2i-j$ then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$4$
B.	$\vert A - I \vert$ , I is identity matrix	II.	$-7$
C.	minor of $a_{32}$	III.	$0$
D.	cofactor $a_{32}$	IV.	$-4$

Choose the correct answer from the options given below:

The number of all different possible matrices of order 2×22 \times 22×2 with each entry −1-1−1, 000 or 111 is :