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Question
For a invertible matrix A if A(adjA) = `[(10, 0),(0, 10)]`, then |A| = ______.
Options
100
–100
10
–10
MCQ
Fill in the Blanks
Solution
For a invertible matrix A if A(adjA) = `[(10, 0),(0, 10)]`, then |A| = 10.
Explanation:
We have,
A(adjA) = `[(10, 0),(0, 10)] = 10[(1, 0),(0, 1)]` = 10I
As, A(adjA) = |A| I
After comparing on both sides, we get
|A| = 10
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