If A ⋅ adj(A) =
[ -2 0 0 ]
[ 0 -2 0 ]
[ 0 0 -2 ], then |adj(A)| equals:
[ 0 -2 0 ]
[ 0 0 -2 ], then |adj(A)| equals:
- -2
- -4
- 4
- 8
The Correct Option is C
Solution and Explanation
We know the identity:
A ⋅ adj(A) = |A| ⋅ I
⇒ |A| ⋅ I = [ -2 0 0 ]
[ 0 -2 0 ]
[ 0 0 -2 ]
⇒ |A| = -2
Also, for a 3 × 3 matrix,
|adj(A)| = |A|^(n-1) = |A|² = (-2)² = 4
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