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Question
If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is ______
Options
a3
a6
a9
a27
MCQ
Fill in the Blanks
Solution
If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is a9.
Explanation:
|A| = a3
|A| |adj A| = |A (adj A)| = |A| I
= `|(|A|, 0, 0), (0, |A|, 0), (0, 0, |A|)| = |A|^3 = (a^3)^3 = a^9`
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