[tex]\displaystyle\\A=\left(\begin{array}{cc}a+1&-b+2\\b-2&a+1\end{array}\right),~a,b\in Z\\\\\det A=(a+1)(a+1)-(-b+2)(b-2)\\\\\det A=(a+1)(a+1)-(-(b-2))(b-2)\\\\\det A=(a+1)(a+1)+(b-2)(b-2)\\\\\boxed{\det A=(a+1)^2+(b-2)^2}\\\\a)~~a=0~\text{si}~b=-1\\\\\implies~\det A=(a+1)^2+(b-2)^2=(0+1)^2+(-1-2)^2=1+9=\boxed{\bf10}\\\\b)~~a=?~\text{si}~b=?~~\text{daca }~\det A=0\\\\\det A=(a+1)^2+(b-2)^2}=0\\\\\implies~~a+1=0~\text{si}~b-2=0\\\\\implies~~\boxed{\boxed{a=-1}~\text{si}~\boxed{b=2}}[/tex]
