# 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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## 1 Answer

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

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thank you very much, I wasn´t sure if the matrices had the asociativity property (first lesson about this). And I was seeing it the whole wrong way :D – chubakueno Aug 14 '12 at 1:00
@chubakueno, yes, the associativity holds but the commutative, does not. Try to find out a counter-example. If you agree, please, accept the answer. – Sigur Aug 14 '12 at 1:02
In some minutes I will, the web doesn´t allow me to do so now. – chubakueno Aug 14 '12 at 1:03
and note that while matrix multiplication may not be commutative, matrix addition is. – Henry Aug 14 '12 at 1:04
I've just formated the text using TeX but somebody should review it and accept it. – Sigur Aug 14 '12 at 1:07