The product of the matrices is an identity matrix. Therefore, X and A are inverse of each other.
The matrices are given as:
[tex]X = \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right][/tex]
[tex]A = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right][/tex]
To check the matrices are inverse, we calculate their products.
[tex]A \times X = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right] \times \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right][/tex]
Multiply the rows of A by the column of X.
This gives
[tex]A \times X = \left[\begin{array}{cc}\frac 15 \times -1 + \frac{3}{10} \times 4&\frac 15 \times -3 + \frac{3}{10} \times 2\\ -\frac 25 \times -1 - \frac{1}{10} \times 4&-\frac 25 \times -3 + -\frac{1}{10} \times 2\end{array}\right][/tex]
[tex]A \times X = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
The product of A and X is an identity matrix.
This means that; both matrix are inverse of each other
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