Given A=[1259]\displaystyle {A}={\left[\begin{array}{cc} {1}&-{2}\\{5}&-{9}\end{array}\right]}  and B=[9251]\displaystyle {B}={\left[\begin{array}{cc} -{9}&{2}\\-{5}&{1}\end{array}\right]} , determine whether A\displaystyle {A} and B\displaystyle {B}  are inverses.

 

AB=\displaystyle {A}{B}= 

 
 

BA=\displaystyle {B}{A}= 

 
 

Are A\displaystyle {A} and B\displaystyle {B} inverses?