Hi everyone I've been messing with a problem with matrices and I can't get it to work. I think I am not seeing it the right way because else I get an 8 variable quadratic system of equations.
If $A$ and $B$ are $2\times 2$ matrices and $A^2 = B^2 = I$ and $AB = \begin{pmatrix} 0 & -1 \\ 1 & 2 \end{pmatrix}$ and $BA = \begin{pmatrix} 2 & 1 \\ -1 & 0 \end{pmatrix}$
calculate $(A+B)^2$.
Any help will be very appreciated