Question

C) What condition can you impose on A and B so that(A+B)(A−B) = A2−B2?

Answer 1

Answer:

Observe that

$(A+B)(A-B)=AA-AB+BA-BB=A^2-AB+BA-B^2$

Since the product of matrices isn't commutative, then for any matrices A and B $A\neq B$.

Then, if we want that $(A+B)(A-B)=A^2-B^2$, we need impose the condition that $AB=BA$