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Question
Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`
Solution
|A| = cos θ (cos θ) – sin θ (– sin θ)
= cos2θ + sin2θ
= 1 ≠ 0
∴ A–1 exists.
A11 = (–1)1+1 M11 = M11 = cos θ
A12 = (–1)1+2 M12 = – M12 = sin θ
A21 = (–1)2+1 M21 = – M21 = – sin θ
A22 = (–1)2+2 M22 = M22 = cos θ
∴ adj (A) = `[(cos theta, sin theta),(-sin theta, cos theta)]^"T"`
= `[(cos theta, -sin theta),(sintheta, cos theta)]`
∴ A–1 = `1/|"A"|` adj (A)
= `[(cos theta, -sin theta),(sin theta, cos theta)]`
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