Question Number 112906 by mohammad17 last updated on 10/Sep/20
$${prove}\:{that}\:\left({B}^{−\mathrm{1}} \right)\left({A}^{−\mathrm{1}} \right)=\left({AB}\right)^{−\mathrm{1}} \:{if}\:{A}=\left(\mathrm{34},\mathrm{12}\right),{B}=\left(\mathrm{12},−\mathrm{13}\right) \\ $$$${please}\:{sir}\:{help}\:{me} \\ $$
Commented by mohammad17 last updated on 10/Sep/20
$${help}\:{me}\:{sir} \\ $$
Commented by mohammad17 last updated on 10/Sep/20
$${yes}\:{sir} \\ $$
Commented by kaivan.ahmadi last updated on 10/Sep/20
$${for}\:{every}\:{A},{B}\:{we}\:{have}\:\left({AB}\right)^{−\mathrm{1}} ={B}^{−\mathrm{1}} {A}^{−\mathrm{1}\:} {since} \\ $$$$\left({AB}\right)\left({B}^{−\mathrm{1}} {A}^{−\mathrm{1}} \right)={A}\left({BB}^{−\mathrm{1}} \right){A}^{−\mathrm{1}} ={AIA}^{−\mathrm{1}} = \\ $$$${AA}^{−\mathrm{1}} ={I}. \\ $$
Commented by bemath last updated on 10/Sep/20
$$\mathrm{do}\:\mathrm{you}\:\mathrm{meant}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{matrix}? \\ $$