[tex]\text{Conditia ca matricea A(m) sa fie inversabila este ca det\big(A(m)\big) sa fie } \\ \text{diferit de 0.} \\ \\ \Rightarrow det\big(A(m)\big) \neq 0 \Rightarrow \left|\begin{array}{cc}m-1&-1\\2&m-2\end{array}\right| \neq 0 \Rightarrow \\ \\ \Rightarrow (m-1)(m-2)-(-2) \neq 0 \Rightarrow (m-1)(m-2) +2 \neq 0 \Rightarrow \\ \\ \Rightarrow m^2-2m-m+2+2\neq 0 \Rightarrow m^2-3m+4\neq 0 \\ \\ \Delta = (-3)^2-4\cdot 1\cdot 4 = 9-16 = 0 \Rightarrow \Delta \ \textless \ 0 [/tex]
[tex]\Rightarrow m^2-3m+4\neq 0, \quad \forall $ $ m \in \mathbb_{R}$ \\ \\ \Rightarrow \boxed{m\in \mathbb_{R} }[/tex]
