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Question
If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
Options
AT
A2
A
I
MCQ
Fill in the Blanks
Solution
If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is AT.
Explanation:
|A| = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)] = -1 ≠ 0`
adj A = `[(0, -1, 0), (1, 0, 0), (0, 0, 1)]`
∴ `A^-1 = 1/|A|`(adj A)
= `[(0, 1, 0), (-1, 0, 0), (0, 0, -1)] = A^T`
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