a$)$ Calculate the determinant of matrix A$.$ Problem $10\mathrm{.}14$

Recall that no all matrices have an inverse. A matrix is singular $($i$.$e$.,$ it doesn't have an inverse$)$ if its determinant equals $0($i$.$e$.,|A|=0).$ Use the

determinant function to test whether each of the following matrices has an inverse. If an inverse exists, compute it$.$

$A=\left[\begin{array}{ccc}2& -1\text{;}& 5\end{array}\right]$

$2$;

$B=\left[\begin{array}{ccc}4& 2\text{;}& 1\end{array}\right]$

$2$;

$C=\left[\begin{array}{ccccccc}2& 0& 0\text{;}& 2& 2\text{;}& -4& 0\end{array}\right]$

$5$

$1$;

a$)$ Calculate the determinant of matrix A$.$ Store it in det$\_$A$.$

b$)$ If matrix A has an inverse, store it in inv$\_$A$.$ Otherwise $($if no inverse exists$)$ store $0$ in inv$\_$A$.$

c$)$ Calculate the determinant of matrix B$.$ Store it in det$\_$B$.$

d$)$ If matrix A has an inverse, store it in inv$\_$B$.$ Otherwise $($if no inverse exists$)$ store $0$ in inv$\_$B$.$

e$)$ Calculate the determinant of matrix C$.$ Store it in det$\_$C$.$

f$)$ If matrix A has an inverse, store it in inv$\_$C$.$ Otherwise $($if no inverse exists$)$ store $0$ in inv$\_$C$.$Store it in det$\_$A$.$

b$)$ If matrix A has an inverse, store it in inv$\_$A$.$ Otherwise $($if no inverse exists$)$ store $0$ in inv$\_$A$.$

c$)$ Calculate the determinant of matrix B$.$ Store it in det$\_$B$.$