If $A, B$ are two square matrices such that $A B=A$ and $B A=B$, then\

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Professor PC Thomas Classes · Answer

(a) Consider $(\mathrm{ABA})=(\mathrm{AB}) \mathrm{A}=\mathrm{A}^{2}$\ Also $\mathrm{ABA}=\mathrm{A}(\mathrm{BA})=\mathrm{AB}=\mathrm{A}$\ $A^{2}=A \Rightarrow A$ is idempotent\ Similarly B is also idempotent