Question

why is this not valid for matrices
(A+B)(A+B)=A^2+2AB+B^2

Answer 1

does AB = BA for matrices?

Answer 2

i am not sure does it?

Answer 3

See property 1 in http://en.wikipedia.org/wiki/Matrix_multiplication#Properties_of_matrix_multiplication

Answer 4

so i doesnt equal

Answer 5

Yes. the question even hints at the problem: why is this not valid for matrices
so you know something is wrong. AB≠BA is a good guess.
when you multiply out
(A+B)(A+B) you get A*A + A*B + B*A +B*B
if A and B were numbers then A*B is the same as B*A and you could combine them
but matrices don't let you do that

Answer 6

so how do i show this by picking a random matrix and show that AB not equal to BA

Answer 7

try
\[\left[\begin{matrix}1 & 2 \\ 1 & 1\end{matrix}\right]\]
and
\[\left[\begin{matrix}1 & 1 \\ 1 & 0\end{matrix}\right]\]