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If for suitab...

Question

If for suitable matrices $A, B$ ; $A B = A$ and $B A = B$ ; then $A^{2}$ equals-

A

I

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B

A

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C

B

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D

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Solution

The correct options are
B $A$
C $B$
Taking $A B = A$

Multiplying by a matrix $A$

$A B A = A^{2}$

$\Rightarrow A (B A) = A^{2}$ (Associative property)

$A B = A^{2}$ ( $∵ B A = B$ )

$\Rightarrow A = A^{2}$ ( $∵ A B = A$ )

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