Die erste binomische Formel gilt nicht, da beispielsweise

${\displaystyle {}{\begin{aligned}{\left({\begin{pmatrix}0&1\\1&0\end{pmatrix}}+{\begin{pmatrix}1&0\\0&0\end{pmatrix}}\right)}^{2}&={\begin{pmatrix}1&1\\1&0\end{pmatrix}}^{2}\\&={\begin{pmatrix}2&1\\1&1\end{pmatrix}},\end{aligned}}}$

aber

${\displaystyle {}{\begin{aligned}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}^{2}+2{\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}1&0\\0&0\end{pmatrix}}+{\begin{pmatrix}1&0\\0&0\end{pmatrix}}^{2}&={\begin{pmatrix}1&0\\0&1\end{pmatrix}}+2{\begin{pmatrix}0&0\\1&0\end{pmatrix}}+{\begin{pmatrix}1&0\\0&0\end{pmatrix}}\\&={\begin{pmatrix}2&0\\2&1\end{pmatrix}}\end{aligned}}}$