Given A=[1413]\displaystyle {A}={\left[\begin{array}{cc} -{1}&{4}\\-{1}&{3}\end{array}\right]} and B=[3411]\displaystyle {B}={\left[\begin{array}{cc} {3}&-{4}\\{1}&-{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?