If A and B are 3 times 3 matrices such that A | vedclass

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(C) Given that $AB = A$ and $BA = B$. To find $A^2$,we have $A^2 = A 	imes A$. Substituting $A = AB$,we get $A^2 = A(AB) = (AA)B$. This does not imme

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$A^2 = A$ and $B^2 = B$

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(C) Given that $AB = A$ and $BA = B$. To find $A^2$,we have $A^2 = A 	imes A$. Substituting $A = AB$,we get $A^2 = A(AB) = (AA)B$. This does not immediately simplify,so let us use the given equations directly. $A^2 = A 	imes A = (AB) 	imes A = A(BA)$. Since $BA = B$,we have $A^2 = AB$. Since $AB = A$,it follows that $A^2 = A$. Similarly,for $B^2$,we have $B^2 = B 	imes B = (BA) 	imes B = B(AB)$. Since $AB = A$,we have $B^2 = BA$. Since $BA = B$,it follows that $B^2 = B$. Therefore,$A^2 = A$ and $B^2 = B$.

If $A$ and $B$ are $3 \times 3$ matrices such that $AB = A$ and $BA = B$,then

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