Question

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

Answer 1

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\\eq B`.

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