[tex] A+B= \left(\begin{array}{cc}1&-1\\0&1\end{array}\right)+\left(\begin{array}{cc}x&-1\\0&x\end{array}\right)=\left(\begin{array}{cc}1+x&-2\\0&1+x\end{array}\right)[/tex]
[tex]det(A+B)=\left|\begin{array}{cc}1+x&-2\\0&1+x\end{array}\right|= (1+x)^{2} +0=(1+x)^{2}[/tex]
[tex] (1+x)^{2} =0 =\ \textgreater \ 1+x=0 =\ \textgreater \ x=-1 [/tex]
