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 .


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