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). ​

Question

If A^-1 = \(\begin{bmatrix} 3 &-1 &1 \\[0.3em] -15 & 6 &-5 \\[0.3em] 5 &-2 & 2 \end{bmatrix}\)and B = \(\begin{bmatrix} 1 &2 &-2 \\[0.3em] -1 & 3 &0 \\[0.3em] 0 &-2 & 1 \end{bmatrix}\), find (AB)^-1.

Answer 1

For B^-1

|B| = \(\begin{vmatrix} 1 &2 &-2 \\[0.3em] -1 & 3 &0 \\[0.3em] 0 &-2 & 1 \end{vmatrix}\)

i.e., B is invertible matrix

⇒ B^-1 exists and have unique solution.