If A, B are two n × n non-singular matrices, then


If $A, B$ are two $n \times n$ non-singular matrices, then

(a) $A B$ is non-singular

(b) $A B$ is singular

(c) $(A B)^{-1} A^{-1} B^{-1}$

(d) $(A B)^{-1}$ does not exist


(a) $A B$ is non-singular

$A$ and $B$ are non-singular matrices of order $n \times n$.

$\therefore|\mathrm{A}| \neq 0$ and $|\mathrm{B}| \neq 0 \quad \ldots(1)$

$A$ and $B$ are of the same order, so $A B$ is defined and is of the same order.



$\Rightarrow|\mathrm{AB}| \neq 0 \quad[$ Using $(1)]$

Thus, $A B$ is non-singular.

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