The identity matrix is the following.
[tex]\begin{bmatrix}{1} & {0} & {} \\ {0} & {1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]
We need to compute the product to find out whether it gives an identity matrix.
[tex]\begin{bmatrix}{1} & {-3} & {} \\ {4} & {2} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{\frac{1}{5}} & {\frac{3}{10}} & {} \\ {-\frac{2}{5}} & {\frac{1}{10}} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{\frac{7}{5}} & {0} & {} \\ {0} & {\frac{7}{5}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]
The result is not an identity matrix; therefore, the product of matrices is not an idenity matrix. Therefore, X and A are not inverse of each other.
