If matrix A=bmatrix 5 & 2 & 3 \\ 4 & 1 & 2 \\ 7 & 6 & 0 bmatrix, then Match the LIST-I with LIST-II, LIST-I, LIST-II, A., A, I., 16, B., Minor of a_23, II., 27, C., Cofactor of a_32, III., 19, D., If a_23 is interchanged with a_32, then A, IV., 2, Choose the correct answer from the options given below: Option 1: A-IV, B-III, C-II, D-I Option 2: A-III, B-IV, C-I, D-II Option 3: A-III, B-I, C-IV, D-II Option 4: A-IV, B-II, C-I, D-III

Answer: A-III, B-I, C-IV, D-II. Solution: A, = 5(-12) - 2(-14) + 3(17) = 19 (III). Minor of a_23 deletes row 2 and column 3: vmatrix5&2\\7&6vmatrix = 16 (I). Minor of a_32 is vmatrix5&3\\4&2vmatrix = -2, and the cofactor is (-1)^5(-2) = 2 (IV). After swapping a_23 and a_32, the determinant becomes 27 (II).

Algebra

Matrices & Determinants

Hard

applied

If matrix $A=\begin{bmatrix} 5 & 2 & 3 \\ 4 & 1 & 2 \\ 7 & 6 & 0 \end{bmatrix}$ , then

Match the LIST-I with LIST-II

LIST-I LIST-II
A. $\vert A \vert$ I. $16$
B. Minor of $a_{23}$ II. $27$
C. Cofactor of $a_{32}$ III. $19$
D. If $a_{23}$ is interchanged with $a_{32}$ , then $\vert A \vert$ IV. $2$

Choose the correct answer from the options given below:

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$16$
B.	Minor of $a_{23}$	II.	$27$
C.	Cofactor of $a_{32}$	III.	$19$
D.	If $a_{23}$ is interchanged with $a_{32}$ , then $\vert A \vert$	IV.	$2$

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

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

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

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

✅ Correct Option: 3

$|A| = 5(-12) - 2(-14) + 3(17) = 19$ (III).

Minor of $a_{23}$ deletes row 2 and column 3: $\begin{vmatrix}5&2\\7&6\end{vmatrix} = 16$ (I).

Minor of $a_{32}$ is $\begin{vmatrix}5&3\\4&2\end{vmatrix} = -2$ , and the cofactor is $(-1)^{5}(-2) = 2$ (IV).

After swapping $a_{23}$ and $a_{32}$ , the determinant becomes 27 (II).

2026: 19 May Shift 2

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ , then $A^{26}$ is equal to

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:

2022: 16 July Shift 2

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}$ , then which of the following is the value of $(\text{adj } A)^{-1}$

2026: 30 May Shift 1

If $A$ is a square matrix of order 3 such that $A(adj\,A)=\begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$ , then which of the following is NOT correct?

2026: 18 May Shift 2

For the matrix $A=\begin{bmatrix} 0 & 0 & 5 \\ 0 & 6 & 0 \\ 7 & 0 & 0 \end{bmatrix}$ , which of the following statement(s) is/are TRUE ?

A. $A$ is a scalar matrix.

B. $A$ is a diagonal matrix.

C. $A$ is a square matrix.

D. $A$ is a skew symmetric matrix.

Choose the correct answer from the options given below:

2025: 27 May Shift 1

If A is a square matrix such that $A^2 = A$ and I is the identity matrix of the same order as A, then $(I+A)^2-3A$ is equal to

Solution

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