explain why each of the following algebraic rules will not work in general when the real numbers a and b are replaced by nxn matrices A and B.
a) (a + b)^2 = a^2 +2ab + b^2
b) (a + b) (a - b) = a^2 - b^2
for a) I think the reason is because AB does not equal BA so 2ab makes no sense
But for b) I feel like its the same reason.
if you FOIL it with A and B matrices you get
AA -AB +BA -BB
So it again doesn't make sense with matrices since
(A+B)(A-B) doesn't equal (A-B)(A+B)
is this right?