IMathAS-libretexts

Assuming that A and B are both invertible matrices of the same size, which of the following is $\displaystyle {\left({A}{B}\right)}^{{-{{1}}}}$ ?

$\displaystyle {A}^{{T}}\cdot{B}^{{T}}$
$\displaystyle {B}^{{-{{1}}}}\cdot{A}^{{-{{1}}}}$
$\displaystyle {B}^{{T}}\cdot{A}^{{T}}$
$\displaystyle {A}^{{-{{1}}}}\cdot{B}^{{-{{1}}}}$