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Question
If A is invertible matrix of order 3 and |A| = 5, then find |adj A|
Solution
We know that A−1 = `1/|"A"|` adj (A)
∴ A−1 |A| = adj (A)
∴ AA−1 |A| = A adj (A)
∴ I |A| = A adj (A)
∴ det (I |A|) = det (A adj (A))
∴ det (I|A|) = det (A) (adj (A))
∴ `|(5, 0, 0),(0, 5, 0),(0, 0, 5)|` = 5 |adj A|
∴ 53 = 5 |adj A|
∴ |adj A| = 52 = 25
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