If A and B are square matrices of the same order, then (A + B) (A

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Multiplication of Matrices

Question

If A and B are square matrices of the same order, then (A + B) (A – B) is equal to

A² – BA + B² + AB

A² – BA – AB – B²

A² – B²

A² – B² + BA – AB

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(A + B) (A – B) = A(A – B) + B(A – B).........because matrix product is distributive.

= A² – AB + BA – B²

And as matrix product is not commutative, so AB ≠ BA

Hence option C is correct.