Question

For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.

Answer 1

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