If vmatrixx&2\\18&xvmatrix = vmatrix6&2\\18&6vmatrix, then x equals: Option 1: 0 Option 2: 6 Option 3: -6 Option 4: ±6

Answer: ±6. Solution: The right side is 36-36=0, and the left side is x^2-36. So x^2=36, giving x=±6.

Algebra

Matrices & Determinants

Easy

core

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$ , then x equals:

-6

±6

✅ Correct Option: 4

The right side is $36-36=0$ , and the left side is $x^2-36$ . So $x^2=36$ , giving $x=\pm6$ .

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Matrix)		LIST-II (Type of matrix)
A.	$A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0\ \forall\, i \neq j$	I.	Scalar matrix
B.	$A = [a_{ij}]_{m \times 1}$	II.	Diagonal matrix
C.	$A = [a_{ij}]_{1 \times n}$	III.	Column matrix
D.	$A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0\ \forall\, i \neq j$ and $a_{ij} = k\ \forall\, i = j, k \neq 0$	IV.	Row matrix

Choose the correct answer from the options given below:

2025: 27 May Shift 1

For the system of linear equations

$x + y + z = 5000$

$6x + 7y + 8z = 35800$

$6x + 7y - 8z = 7000$

the values of x, y and z are:

2025: 2 June Shift 1

if $A = \begin{bmatrix}1 & 0\\3 & 1\end{bmatrix}$ and $A^4 = \begin{bmatrix}1 & 0\\k & 1\end{bmatrix}$ then value of $k$ is

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) If $A = [a_{ij}]_{n \times n}$ , where $a_{ij} = \begin{cases}0, & i \ne j \\ k, & i=j, k\ne 0\end{cases}$ then A is ___	(I) Symmetric matrix
(B) If $A = [a_{ij}]_{2\times 2}$ , where $a_{ij} = \begin{cases}1, & i \ne j \\ 0, & i=j\end{cases}$ , then $A^2$ is ___	(II) Skew-Symmetric matrix
(C) If A and B are matrices of the same order, then $(AB^T - BA^T)$ is ___	(III) Identity matrix
(D) If A and B are symmetric matrices of the same order, then $(AB+BA)$ is ___	(IV) Scalar matrix

Choose the correct answer from the options given below:

2026: 30 May Shift 2

If A and B are symmetric matrices of same order, then which of the following statements are true?

(A) $AB^T+B^TA$ is a skew-symmetric matrix.

(B) $AB^T-BA^T$ is a skew-symmetric matrix

(D) $(AB)^{-1}(BA)^T=A$

Choose the correct answer from the options given below:

2025: 3 June Shift 1

If $A = [a_{ij}]$ is skew symmetric matrix of order 'n', then