$${f$$ A and B are two matrices such that AB $$=$$ A and A $$=$$ B, then $$B2$$ is equal to

Question

$${f$$ A and B are two matrices such that AB $$=$$ A and A $$=$$ B, then $$B2$$ is equal to

Infinity Learn · Accepted Answer

We have, $$AB=$$ A and $$BA=$$ B∴    $$B2$$    $$=BB$$        ⇔    $$B2$$    $$=(BA)B$$        ⇒    $$B2$$    $$=B(AB)$$                          [∵$$BA=B$$]⇒    $$B2$$    $$=BA$$        ⇒    $$B2$$    $$=B$$                                  [∵$$AB=A$$]⇒  $$B2=B$$                                         [∵$$BA=B$$]

{f $A$ and $B$ are two matrices such that $A B = A$ and $A = B,$ then $B^{2}$ is equal to

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{f A and B are two matrices such that AB = A and A = B, then B2 is equal to

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{f $A$ and $B$ are two matrices such that $A B = A$ and $A = B,$ then $B^{2}$ is equal to