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I am trying to solve chain matrices multiplication. Where I encounter a problem, which sees like dead end to me. How further I can decompose $X^{-1} . Y . X = Z$ or simplify it to find matrix $X$ from this multiplication.

Where matrices $X,Y$and $Z$ are 2x2 non-singular matrices.

Any help will be appreciated.

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    Intuitively, it represents a basis change. The matrix $Y$ represented in another basis (which is represented by $X$, is $Z$. This makes sense only when $X,Y,Z$ are square matrixes.2012-12-17

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