MCQ
If $A, B$ are two $n \times n$ non-singular matrices, then
- ✓$AB$ is non-singular.
- B$AB$ is singular.
- C$(AB)^{-1} A^{-1} B^{-1}.$
- D$(AB)^{-1}$ does not exist.
$A$ and $B$ are non-singular matrices of order $n \times n.$
$\therefore|\text{A}|\neq0\text{ and }|\text{B}|\neq0\ .....(\text{i})$
$A$ and $B$ are of the same order, so $AB$ is defined and is of the same order.
Thus,
$|AB| = |A||B|$
$\Rightarrow|\text{AB}|\neq0\ \big[\text{Using (1)}\big]$
Thus, $Ab$ is non-singular.
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