Let A and B be square matrices of order 3 and k is a constant. If |A| ≠ 0 and |B| ≠ 0, where |A| represents the determinant of A, then which of the following statements are true ? (where A' denotes the transpose of matrix A) (A) (AB)^-1 = B^-1 A^-1 (B) (A+B)' = A' x B' (C) (AB)' = A'B' (D) |kA| = k^3 |A| (E) |A'| = |A| Choose the correct answer from the options given below :

Question

Option 1: (A), (B), (D) only

Option 2: (A), (D), (E) only

Option 3: (B), (C), (D) only

Option 4: (B), (C), (E) only

AfterBoards · Accepted Answer

The answer is '(A), (D), (E) only'. View full solution:

List-I	List-II
(Matrix)	(Determinant)
(A) $\begin{bmatrix} 1 & 7 \\ -3 & 5 \end{bmatrix}$	(I) 24
(B) $\begin{bmatrix} -2 & 5 \\ -3 & -3 \end{bmatrix}$	(II) 32
(C) $\begin{bmatrix} -12 & 8 \\ -16 & 8 \end{bmatrix}$	(III) 21
(D) $\begin{bmatrix} 15 & 9 \\ -21 & -11 \end{bmatrix}$	(IV) 26

CUET Mathematics 2022 7 Aug Shift 2 PYQs

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