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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
up vote 3 down vote accepted

Matrix multiplication is associative, that is given matrices $A,B$ and $C$,

$$A(BC)=(AB)C.$$

So the order in which you carry out the multiplication does not matter, you will get the same result.

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