Question

For two square matrices A and B of the same order, $(A+B)(A-B)$ = $A^2–B^2$.

• A. True
• B. False

Answer 1

The correct option is B

False

Given that A and B are square matrices of the same order.
$(A+B)(A-B)=A^2-AB+BA–B^2$---------(1)
We know that matrix multiplication is not commutative.
i.e, $AB\ne BA$ --------(2)
So using (1) and (2) for a geenral case,
$(A+B)(A-B)\ne A^2–B^2$.
Therefor the given statement is false.