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Question
If A = `[(3, 1),(5, 2)]`, and AB = BA = I, then find the matrix B
Solution
AB = BA = I
⇒ B = A−1
|A| = `|(3, 1),(5, 2)|`
= 6 – 5
= 1
∴ A11 = (–1)1+1 M11 = M11 = 2
A12 = (–1)1+2 M12 = – M12 = – 5
A21 = (–1)2+1 M21 = – M21 = – 1
A22 = (–1)2+2 M22 = M22 = 3
∴ adj (A) = `[(2, -5),(-1, 3)]^"T"`
= `[(2, -1),(-5, 3)]`
∴ B = A−1 = `1/|"A"|` adj (A)
∴ B = `[(2, -1),(-5, 3)]`
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