(A) (AB)−1=B−1A−1 is a standard property, true.
(B) (A+B)′=A′+B′, not A′×B′, false.
(C) (AB)′=B′A′, not A′B′, false.
(D) ∣kA∣=kn∣A∣=k3∣A∣ for n=3, true.
(E) ∣A′∣=∣A∣ is a standard property, true.
So (A), (D), (E) are correct.
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…
CUET UG 2022 — Mathematics Algebra
2022mcqeasy
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−1A−1
(B) (A+B)′=A′×B′
(C) (AB)′=A′B′
(D) ∣kA∣=k3∣A∣
(E) ∣A′∣=∣A∣
Choose the correct answer from the options given below :
Official previous-year question
Held on 7 Aug 2022 · Verified 13 Jul 2026.
Options
- A
(A), (B), (D) only
- B
(A), (D), (E) only
- C
(B), (C), (D) only
- D
(B), (C), (E) only
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