📘 Question
If \(A\) and \(B\) are square matrices of the same order, find:
\[
(A + B)(A – B)
\]
(a) \(A^2 – B^2\)
(b) \(A^2 – BA – AB – B^2\)
(c) \(A^2 – B^2 + BA – AB\)
(d) \(A^2 – BA + B^2 + AB\)
✏️ Step-by-Step Solution
Step 1: Expand using distributive law
\[
(A + B)(A – B) = A(A – B) + B(A – B)
\]
—
Step 2: Multiply terms
\[
= A^2 – AB + BA – B^2
\]
—
Step 3: Rearrange
\[
= A^2 – B^2 + BA – AB
\]
—
✅ Final Answer
\[
\boxed{(c)\; A^2 – B^2 + BA – AB}
\]
—
💡 Key Concept
Matrix multiplication is not commutative:
\[
AB \ne BA
\]
So,
\[
(A+B)(A-B) \ne A^2 – B^2
\]