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Question

A square matrix A is said to be an idempotent matrix if A2=A. If A and B are idempotent matrices and AB=BA, then which of the following is an idempotent matrix

A
A+B
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B
AB
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C
AB
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D
BA
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Solution

The correct option is B AB
A and B are idempotent matrices and AB=BAi.e A2=A and B2=B(AB)2 = (AB)(AB) =A(BA)B=A(AB)B=(AA)(BB)(AB)2=ABHence,AB is an idempotent matrix.

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