MathDB

[*]Give an example of matrices

A

and

B

from

\mathcal{M}_{2}(\mathbb{R})

, such that A^{2}+B^{2}=\left( \begin{array} [c]{cc} 2 & 3\\ 3 & 2 \end{array} \right) . [*]Let

A

and

B

be matrices from

\mathcal{M}_{2}(\mathbb{R})

, such that \displaystyle A^{2}+B^{2}=\left( \begin{array} [c]{cc} 2 & 3\\ 3 & 2 \end{array} \right) . Prove that

AB\neq BA

Problem Statement