Let A be a 3 x 3 non-singular matrix such that adj A = adj A^-1, then the value of | A | equals to:
A)1 B) - 1 C) +-1 D) +- 2
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Answer:
Correct option is
A
∣A∣A
Step-by-step explanation:
As A is a non-singular matrix, A is invertible and A
−1 = ∣A∣ adjA
⇒adjA=∣A∣A −1
=B(say).
Now,
adj(adjA)=adj(B)=∣B∣B
−1
=
∣
∣
∣
∣A∣A
−1
∣
∣
∣
(∣A∣A
−1
)
−1
=∣A∣
3
∣A
−1
∣∣A∣
−1
(A
−1
)
−1
[using scalar multiple property of determinants]
=∣A∣
3
∣A∣
1
.
∣A∣
1
A=∣A∣A
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