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

1.	If A and B are square matrices of the same order, then (A + B)(A – B) is equal to :A. A2 – B2 B. A2 – BA – AB – B2 C. A2 – B2 + BA – AB D. A2 – BA + B2 + AB
Answer» (C). A² – B² + BA – AB (A + B)(A – B) = A (A – B) + B (A – B) = A.A – A.B + B.A – B.B =A² – A.B + B.A – B.B = A² – AB + BA – BB Matrix multiplication does not have a commutative property i.e., A.B ≠ B.A Hence, Option (C) is the answer.

If A and B are square matrices of the same order, then (A + B)(A – B) is equal to :A. A2 – B2 B. A2 – BA – AB – B2 C. A2 – B2 + BA – AB D. A2 – BA + B2 + AB

Answer»

(C). A² – B² + BA – AB

(A + B)(A – B) = A (A – B) + B (A – B)

= A.A – A.B + B.A – B.B

=A² – A.B + B.A – B.B

= A² – AB + BA – BB

Matrix multiplication does not have a commutative property

i.e.,

A.B ≠ B.A

Hence,

Option (C) is the answer.

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If A and B are square matrices of the same order, then (A + B)(A – B) is equal to :A. A2 – B2 B. A2 – BA – AB – B2 C. A2 – B2 + BA – AB D. A2 – BA + B2 + AB

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