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(D) If $P$ and $Q$ are non-zero square matrices such that $PQ = 0$,it does not imply that either $P$ or $Q$ must be singular. For example,consider $P

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None of the options are correct

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(D) If $P$ and $Q$ are non-zero square matrices such that $PQ = 0$,it does not imply that either $P$ or $Q$ must be singular. For example,consider $P = \begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix}$ and $Q = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}$. Here,$P 
eq 0$ and $Q 
eq 0$,but $PQ = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} = 0$. In this case,both matrices are singular because their determinants are $0$. However,it is possible for the product of two matrices to be zero without specific constraints on their singularity beyond the fact that they cannot both be non-singular (since if both were non-singular,$PQ$ would be non-singular and thus $PQ 
eq 0$). Since the options provided suggest definitive requirements that are not universally true or are logically flawed,the correct conclusion is that none of the given options are necessarily true.

If $P$ and $Q$ are two non-zero square matrices of the same order such that the product $PQ = 0$,then ........

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