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
A−B
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D
B−A
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Solution
The correct option is BAB AandBareidempotentmatricesandAB=BAi.eA2=AandB2=B(AB)2=(AB)(AB)=A(BA)B=A(AB)B=(AA)(BB)⇒(AB)2=ABHence,ABisanidempotentmatrix.