<s>[INST] Is $(A+B)^2 = A^2 + B^2$ if $A$ and $B$ are matrices If $A$ and $B$ are matrices is $(A+B)^2 = A^2 + B^2$? 
I thought because, $AB + BA = AB - AB = 0$.
 [/INST] $$(A+B)^2 = (A+B)(A+B) = A^2 + AB + BA + B^2 \neq A^2 + B^2$$
$(A+B)^2 = A^2 + B^2$ if and only if $AB + BA = 0 \iff AB = -BA$, but this is not true in general.
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