Match the LIST-I with LIST-II, LIST-I (Matrix A =), LIST-II ( adj A =), A., bmatrix2 & 1\\ 1 & 3bmatrix, I., 3, B., bmatrix1 & 0\\ 3 & 2bmatrix, II., 2, C., bmatrix3 & 0\\ 0 & 1bmatrix, III., 5, D., bmatrix0 & -1\\ 4 & 0bmatrix, IV., 4, Choose the correct answer from the options given below: Option 1: A-III, B-II, C-I, D-IV Option 2: A-II, B-I, C-III, D-IV Option 3: A-I, B-IV, C-II, D-III Option 4: A-IV, B-III, C-I, D-II

Answer: A-III, B-II, C-I, D-IV. Solution: For a 2 x 2 matrix, adj A, =, A, ^(n-1)=, A, . The determinants are 6-1=5 (III), 2-0=2 (II), 3-0=3 (I) and 0+4=4 (IV).

Algebra

Matrices & Determinants

Easy

applied

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:

	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.	$4$

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

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

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

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

✅ Correct Option: 1

For a $2 \times 2$ matrix, $|adj A|=|A|^{n-1}=|A|$ . The determinants are $6-1=5$ (III), $2-0=2$ (II), $3-0=3$ (I) and $0+4=4$ (IV).

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Match List-I with List-II

List-I	List-II
(A) $\left\vert \text{adj}A \right\vert$	(I) $\dfrac{1}{\left\vert A \right\vert}$
(B) $\left\vert A^{-1} \right\vert$	(II) $\left\vert A \right\vert^{4}$
(C) $\left\vert A.\text{adj}A \right\vert$	(III) $\left\vert A \right\vert^{3}$
(D) $\left\vert \text{adj}(\text{adj}A) \right\vert$	(IV) $\left\vert A \right\vert^{2}$

Choose the correct answer from the options given below:

2025: 19 May Shift 1

If matrix $A = \begin{bmatrix} p & -3 \\ -4 & p \end{bmatrix}$ and $|A^3| = 64$ , then the value of p is:

Solution

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