Question Number 107331 by saorey0202 last updated on 10/Aug/20
$$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{an}\:\mathrm{invertible}\:\mathrm{matrix},\:\mathrm{then}\:\mathrm{det}\left({A}^{−\mathrm{1}} \right) \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$
Answered by udaythool last updated on 10/Aug/20
$${AA}^{−\mathrm{1}} ={I} \\ $$$$\Rightarrow\mid{AA}^{−\mathrm{1}} \mid=\mid{A}\mid\centerdot\mid{A}^{−\mathrm{1}} \mid=\mid{I}\mid=\mathrm{1} \\ $$$$\Rightarrow\mid{A}^{−\mathrm{1}} \mid=\frac{\mathrm{1}}{\mid{A}\mid} \\ $$