If $A$ and $B$ are square matrices of order $3$ , $A$ is non-singular and $A B = 0$ , then $B$ is a

n u l l m a t r i x

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s i n g u l a r m a t r i x

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e i t h e r s i n g u l a r o r n o n - s i n g u l a r m a t r i x

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u n i t m a t r i x

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Solution

The correct option is C $e i t h e r s i n g u l a r o r n o n - s i n g u l a r m a t r i x$
If $A$ and $B$ are square matrices of order $43$ . $A$ is non-singular and $A B = 0$ then one may non-singular matrix not both
$\begin{matrix} G i v e n | A B | = 0 | A B | = | A | | B | n o w, w e c o n c l u d e | A | | B | = 0 s o, e i t h e r | A | = 0 o r | B | = 0 ∴ e i t h e r A o r B m u s t b e n o n - sin g u l a r . \end{matrix}$
Hence,option $C$ is the correct answer.

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If A and B are square matrices of order 3, A is non-singular and AB=0, then B is a

If $A$ and $B$ are square matrices of order $3$ , $A$ is non-singular and $A B = 0$ , then $B$ is a