# When X'XAX'X=X'X is satified, show that X'XA'X'X=X'X.

When $X'XAX'X=X'X$ is satified, show that $X'XA'X'X=X'X$.
• $X'$ is a transpose of $X$.

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## 1 Answer

Simply take the transpose of both sides. Since $(AB)'=B'A'$ the result follows, as both strings of matrices get reversed, and then transposed term by term

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