If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y

,

We have the matrix equations,

…(i)

…(ii)

Subtracting equation (i) from (ii), we get

…(iii)

Adding equations (i) and (ii), we get

…(iv)

Adding equations (iii) and (iv), we get

Putting the matrix A in equation (iv), we get

Thus, and .