X ∈ M₂ ⇒ [tex] \left[\begin{array}{ccc}a&b\\c&d\end{array}\right] [/tex]
A · X = [tex] \left[\begin{array}{ccc}1&1\\1&1\end{array}\right] [/tex] · [tex] \left[\begin{array}{ccc}a&b\\c&d\end{array}\right] [/tex] = [tex] \left[\begin{array}{ccc}a+c&b+d\\a+c&b+d\end{array}\right] [/tex]
(A · X) · B = [tex] \left[\begin{array}{ccc}a+c&b+d\\a+c&b+d\end{array}\right] [/tex] · [tex] \left[\begin{array}{ccc}1&-1\\1&-1\end{array}\right] [/tex] = [tex] \left[\begin{array}{ccc}a+c+b+d&-a-c-b-d\\a+c+b+d&-a-b-c-d\end{array}\right] [/tex]
Deci A · X · B = O₂ ⇒ [tex] \left[\begin{array}{ccc}a+c+d+b&-a-b-c-d\\a+b+c+d&-a-b-c-d\end{array}\right] [/tex] = [tex] \left[\begin{array} {ccc}0&0\\0&0\end{array}\right] [/tex] ⇒ suma elementelor din matricea X, adica a+b+c+d=0
