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(B) Given that $AB = O$ and $B$ is a non-singular matrix.Since $B$ is non-singular,its determinant $|B| 
eq 0$,which implies that the inverse matrix

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$A = O$

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(B) Given that $AB = O$ and $B$ is a non-singular matrix.Since $B$ is non-singular,its determinant $|B| 
eq 0$,which implies that the inverse matrix $B^{-1}$ exists.Now,multiply both sides of the equation $AB = O$ by $B^{-1}$ on the right side:$(AB)B^{-1} = OB^{-1}$Using the associative property of matrix multiplication:$A(BB^{-1}) = O$Since $BB^{-1} = I$,where $I$ is the identity matrix:$AI = O$Therefore,$A = O$.

$A$ and $B$ are $n$-rowed square matrices such that $AB = O$ and $B$ is non-singular. Then:

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