Algebra

Matrices & Determinants

Easy

common

If the matrix $A = \begin{bmatrix} -2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is given, then which of the following statements is/are TRUE?

A. A is a square matrix

B. A is a symmetric matrix

C. A is a scalar matrix

D. A is a identity matrix

Choose the correct answer from the options given below:

A, B, C and D

A, B and C only

A and B only

A only

✅ Correct Option: 3

$A$ is $3\times3$ , so it is square. Every diagonal matrix satisfies $a_{ij}=a_{ji}$ , so it is symmetric. A scalar matrix needs all diagonal entries equal, but they are $-2,3,4$ , so it is not scalar and hence not identity. Only A and B hold.

2026: 21 May Shift 2

Let A, B, C be square matrices of equal orders and I be the identity matrix of same order, Then which of the following are TRUE?

A. $(AB)C = A(BC)$

B. $AB = BA$

C. $A(B+C) = AB + AC$

D. $AI = IA = A$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Matrix $A =$ )		LIST-II ( $\vert adj A \vert =$ )
A.	$\begin{bmatrix}2 & 1\\ 1 & 3\end{bmatrix}$	I.	$3$
B.	$\begin{bmatrix}1 & 0\\ 3 & 2\end{bmatrix}$	II.	$2$
C.	$\begin{bmatrix}3 & 0\\ 0 & 1\end{bmatrix}$	III.	$5$
D.	$\begin{bmatrix}0 & -1\\ 4 & 0\end{bmatrix}$	IV.	$4$

Choose the correct answer from the options given below:

2022: 7 Aug Shift 2

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

2026: 18 May Shift 1

If $A$ is a square matrix of order $3 \times 3$ and $|adj\ A| = 4$ , then

Match List-I with List-II

List-I	List-II
(A) $\left\vert A^{-1} \right\vert$	(I) $108$
(B) $\left\vert 3\,\text{adj}A \right\vert$	(II) $\pm\dfrac{1}{2}$
(C) $\left\vert 2A \right\vert$	(III) $\pm8$
(D) $\left\vert A.\text{adj}A \right\vert$	(IV) $\pm16$

Choose the correct answer from the options given below:

2025: 14 May Shift 2

The values of $\lambda$ for which the system of equation $x + 2y + z = 14, - x + y + z = 10, x + \lambda y + z = 2$ has unique solution is

2025: 30 May Shift 1

If $A = \begin{bmatrix} 2 & -2 & 1 \\ 0 & 4 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 & 7 \\ 2 & 0 & 6 \end{bmatrix}$ are two matrices such that $3A - 2B + 4C = 0$ , then matrix $C$ is equal to:

Solution

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