Question 807873
1) (A + B)^2 = A^2 + 2AB + B^2



(A + B)^2 = (A+B)(A+B)


(A + B)^2 = A(A+B) + B(A+B)


(A + B)^2 = A*A+A*B + B*A+B*B


(A + B)^2 = A^2+A*B + B*A+B^2


This as far as we can go. We CANNOT say that A*B = B*A since matrix multiplication is NOT commutative in general.


Therefore (A + B)^2 = A^2 + 2AB + B^2 is false.


=======================================================


2) A(A+B) = A^2 + AB 



A(A+B) = A*A + A*B


A(A+B) = A^2 + AB


So that confirms A(A+B) = A^2 + AB to be true.