# Help with a problem with matrices

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

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Please, type in TeX. Consider $(A+B)^2=(A+B)(A+B)=AA+AB+BA+BB$ and do the math.