Given A=[(5 0 4), (2 3 2), (1 2 1)], B^-1 = [(1 3 3), (1 4 3), (1 3 4)]. Compute (AB)^–1.

Question

Given \(A=\begin{bmatrix}5&0&4\\2&3&2\\1&2&1\end{bmatrix},\)\(B^{-1}=\begin{bmatrix}1&3&3\\1&4&3\\1&3&4\end{bmatrix}.\) Compute (AB) ^–1.

Answer 1

  \(A=\begin{bmatrix}5&0&4\\2&3&2\\1&2&1\end{bmatrix},\)\(B^{-1}=\begin{bmatrix}1&3&3\\1&4&3\\1&3&4\end{bmatrix}\) 

Here , (AB) ^–1 = B ^–1 A ^–1

|A| = – 5 + 4 = – 1

Cofactors of A are:

C₁₁ = – 1 C₂₁ = 8 C₃₁ = – 12

C₁₂ = 0 C₂₂ = 1 C₃₂ = – 2

C₁₃ = 1 C₂₃ = – 10 C₃₃ = 15