If A = [(3 -3 4), (2 -3 4), (0 -1 1)], show that A^–1 = A^3.

Question

If \(A=\begin{bmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{bmatrix}\), 

show that A^–1 = A³.

Answer 1

\(A=\begin{bmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{bmatrix}\)

|A| = 3 + 6 – 8 = 1

Cofactors of A are:

C₁₁ = 1 C₂₁ = – 1 C₃₁ = 0

C₁₂ = – 2 C₂₂ = 3 C₃₂ = – 4

C₁₃ = – 2 C₂₃ = 3 C₃₃ = – 3

Hence, A^–1 = A³