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CBSE Class 12 · 2024 · MatricesMultiple Choice

If

A

is a square matrix of order

3

such that the value of

∣ adj A ∣ = 8

, then the value of

∣ A^{⊤} ∣

is:

(A) $2$
(B) $- 2$
(C)8
(D) $22$ ✓ Correct

Answer: (D)

Solution

For order

3

,

∣ adj A ∣ = ∣ A ∣^{n - 1} = ∣ A ∣^{2} = 8

, so

∣ A ∣ = \pm 22

. Since

∣ A^{⊤} ∣ = ∣ A ∣

and the options are positive,

∣ A^{⊤} ∣ = 22

.
Correct option: (D)

22

.

CBSE Class 12 Board · 2024 · Single correct option

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