Question

If A^-1 = [(3, -1, 1), (-15, 6, -5), (5, -2, 2)] and B = [(1, 2, -2), (-1, 3, 0), (0, -2, 1)], find (AB)^-1.

Answer 1

For B^–1

 = 1(3 – 0) – 2(–1 – 0) – 2(2 – 0 ) = 3 + 2 – 4 = 1 ≠ 0

i.e., B is invertible matrix 

⇒ B^–1 exist. 

A₁₁ = 3, A₁₂ = 1, A₁₃ = 2 

A₂₁ = 2, A₂₂ = 1, A₂₃ = 2 

A₃₁ = 6, A₃₂ = 2, A₃₃ = 5