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  4. Let A and B are two square matrices such that AB=A and BA=B, then A2 equals to:

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Q. Let $ A $ and $ B $ are two square matrices such that $ AB=A $ and $ BA=B, $ then $ {{A}^{2}} $ equals to:

KEAMKEAM 2004

Solution:

$ {{A}^{2}}=A.A=AB.A $ $ =A.BA=AB=A $