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Question
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
Solution
We know that `"A"^-1 = 1/|"A"|` adj (A)
∴ AA−1 = `"A" 1/|"A"|` adj (A)
∴ |A| I = A . (adj (A))
∴ |A| I = `[(10, 0),(0, 10)] =10 [(10, 0),(0, 10)] = 10l`
We know that, A (adj A) = |A|l
On comparing both sides, we get
⇒ |A| = 10
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