Question 49
a) Give an example of matrices $A$ and $B$ from $M_2(\mathbb{R})$, such that
$$
A^2 + B^2 = \begin{pmatrix} 2 & 3 \\ 3 & 2 \end{pmatrix}.
$$
b) Let $A$ and $B$ be matrices from $M_2(\mathbb{R})$, such that $A^2 + B^2 = \begin{pmatrix} 2 & 3 \\ 3 & 2 \end{pmatrix}$. Prove that $AB \neq BA$.
$$
A^2 + B^2 = \begin{pmatrix} 2 & 3 \\ 3 & 2 \end{pmatrix}.
$$
b) Let $A$ and $B$ be matrices from $M_2(\mathbb{R})$, such that $A^2 + B^2 = \begin{pmatrix} 2 & 3 \\ 3 & 2 \end{pmatrix}$. Prove that $AB \neq BA$.