Respuesta :
Answer:
We conclude that A and B are inverses of each other since the product AB gives an identity matrix
Explanation:If A and B are inverses of each other, then
[tex]AB=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex][tex]\begin{gathered} AB=\begin{bmatrix}{3} & {8} \\ {1} & {2}\end{bmatrix}\begin{bmatrix}-{1} & {4} \\ {\frac{1}{2}} & {-\frac{3}{2}}\end{bmatrix} \\ \\ =\begin{bmatrix}{-3+\frac{8}{2}} & 12-\frac{24}{2}{} \\ {-1+\frac{2}{2}} & 4-\frac{6}{2}{}\end{bmatrix} \\ \\ =\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \end{gathered}[/tex]Therefore, we conclude that A and B are inverses of each other.
