Algebra

Matrices & Determinants

Medium

core

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

Match List-I with List-II

List-I List-II
(A) $a_{21}+a_{32}$ (I) 0
(B) $\lvert A\rvert$ (II) 19
(C) Number of the elements in A (III) 7
(D) $a_{22}.a_{31}+a_{21}.a_{33}$ (IV) 9

Choose the correct answer from the options given below:

List-I	List-II
(A) $a_{21}+a_{32}$	(I) 0
(B) $\lvert A\rvert$	(II) 19
(C) Number of the elements in A	(III) 7
(D) $a_{22}.a_{31}+a_{21}.a_{33}$	(IV) 9

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(A) - (III), (B) - (I), (C) - (IV), (D) - (II)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

✅ Correct Option: 3

The rows are $(1,0,-1)$ , $(3,2,1)$ , $(5,4,3)$ . So $a_{21}+a_{32}=3+4=7$ ; the determinant is 0 because the third row equals twice the second minus the first; there are $3\times3=9$ elements; and $a_{22}a_{31}+a_{21}a_{33}=2(5)+3(3)=19$ .

2025: 13 May Shift 1

The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is a

(A) Null matrix

(B) Unit matrix

(D) Skew-symmetric matrix

Choose the correct answer from the options given below:

2026: 19 May Shift 2

If A is a square matrix such that $A^2 = I$ , then $(A+I)^3 + (A-I)^3 - 7A$ is equal to

2025: 27 May Shift 1

If A is a square matrix such that $A^2 = A$ and I is the identity matrix of same order as A, then the value of $(A-2I)^2 - (2A + I)^2 + 11A$ is:

2025: 3 June Shift 2

If $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 3 & 0 \\ 4 & -8 \end{vmatrix}$ , then value(s) of x is/are

2026: 22 May Shift 1

If $adjA=\begin{bmatrix}7 & -3 & 2\\3 & 0 & -3\\-1 & 3 & 1\end{bmatrix}$ , then $A^{-1}$ is:

2025: 27 May Shift 1

Let $A$ be a non-singular square matrix of order $n$ , then

Match List-I with List-II

List-I	List-II
(A) $A(\text{adj} A)$	(I) $\frac{1}{\vert A\vert }$
(B) $\vert \text{adj} A\vert$	(II) $\vert A\vert ^n$
(C) $\vert A^{-1}\vert$	(III) $\vert A\vert I$
(D) $\vert A(\text{adj} A)\vert$	(IV) $\vert A\vert ^{n-1}$

Choose the correct answer from the options given below:

Solution

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