[tex]\displaystyle A+A^t=2I_2 \Leftrightarrow \left[\begin{array}{ccc}2a&b+c\\b+c&2d\\\end{array}\right]= \left[\begin{array}{ccc}2&0\\0&2\end{array}\right] \Rightarrow 2a=2,~b+c=0 \\ \\ si~2d=2.~Deci~a=1,~d=1~si~b+c=0 \Leftrightarrow c=-b. \\ \\ A-A^t= \left[\begin{array}{ccc}0&b-c\\c-b&0 \end{array}\right]= \left[\begin{array}{ccc}0&2b\\-2b&0\end{array}\right]. \\ \\ det(A-A^t)=0 \cdot 0-2b \cdot (-2b)=4b^2~\vdots~4~(deoarece~b \in \mathbb{Z}).[/tex]
