Se observa ca [tex]A^{2} -4A+4I_{2} =O_{2} [/tex] mai poate fi scris ca [tex]A^{2}-2*A*I_{2}-2*A*I_{2}+2^{2}I_{2}^{2}=O_{2}[/tex]. Scotand in factor obtinem [tex]A(A-I_{2})-I_{2}(A-I_{2})=(A-I_{2})*(A-I_{2})=(A-I_{2})^{2}=O_{2}[/tex]
Dam o forma generala matricei A, astfel [tex]A=\left[\begin{array}{ccc}x&y\\y&x\end{array}\right] [/tex]. Neavand cerinta originala, presupun ca e vorba de astfel de matrice.
Revenind la [tex](A-I_{2})^{2}=O_{2}[/tex] si inlocuind pe A cu forma data, se obtine
[tex](\left[\begin{array}{ccc}x&y\\y&x\end{array}\right]-\left[\begin{array}{ccc}2&0\\0&2\end{array}\right])^{2}=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
[tex](\left[\begin{array}{ccc}x-2&y\\y&x-2\end{array}\right])^{2}=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
