(1)IF A and B are square matrices such that $\displaystyle AB=\omega A$ and $\displaystyle BA=\phi B $ where $\displaystyle \phi $ and $\displaystyle \omega $ are non - zero scalars , prove that $\displaystyle A^2=\phi A $and $\displaystyle B^2=\omega B . $

(2) If A is a 2x2 matrix such that $\displaystyle A^2=\omega A$ where $\displaystyle \omega$ is a non-zero scalar , prove that A is either non-singular or $\displaystyle A=\phi I $ where I is an identity .

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