# solving linear matrix equation problem

Given two matrices $X$ and $Y$, with $Y$ invertible. Suppose that

$$X=YZY^{-1}.$$

so

$$Z=Y^{-1}XY.$$

In what order should I do the corresponding matrix multiplications to compute $Z$ ?

Thanks.

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You seem to already have solved for $Z$ by multiplying both sides by $Y^{-1}$ from the left and by $Y$ from the right. – Mårten W Apr 20 '13 at 18:49

Matrix multiplication is associative, that is given matrices $A,B$ and $C$,
$$A(BC)=(AB)C.$$