[tex]B=A\cdot(A+m\cdot I_2)=\left(\begin{array}{cc}-1&1\\0&0\end{array}\right)\cdot\left[\left(\begin{array}{cc}-1&1\\0&0\end{array}\right)+m\cdot\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\right]=\\\\=\left(\begin{array}{cc}-1&1\\0&0\end{array}\right)\cdot\left[\left(\begin{array}{cc}-1&1\\0&0\end{array}\right)+\left(\begin{array}{cc}m&0\\0&m\end{array}\right)\right]=\left(\begin{array}{cc}-1&1\\0&0\end{array}\right)\cdot\left(\begin{array}{cc}m-1&1\\0&m\end{array}\right)=\\\\=\left(\begin{array}{cc}1-m+1\cdot 0&(-1)\cdot1+1\cdot m\\0\cdot(m-1)+0\cdot 0&0\cdot1+0\cdot m\end{array}\right)=\left(\begin{array}{cc}1-m&m-1\\0&0\end{array}\right).[/tex]
Din cele de mai sus detB = 0, deci pentru orice m ∈ R detB=0.
Green eyes.
