When $X^\prime XAX^\prime X=X^\prime X$ is satified, show that $X^\prime XA^\prime X^\prime X=X^\prime X$.

Question

When $X^\prime XAX^\prime X=X^\prime X$ is satified, show that $X^\prime XA^\prime X^\prime X=X^\prime X$.

• $X^\prime$ is the transpose of $X$.

Answer 1

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