If A and B are matrices of same order, under what condition is (A + B)² = A² + 2AB + B² true? A. Always B. Never C. If A = B D. If AB = BA Answer: D) If AB = BA Explanation: Expanding (A + B)² gives (A + B)(A + B) = A² + AB + BA + B². For this to equal A² + 2AB + B², we must have AB = BA (the matrices commute).

imo class 12 matrices

If A and B are matrices of same order, under what condition is (A + B)² = A² + 2AB + B² true?

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If A and B are matrices of same order, under what condition is (A + B)² = A² + 2AB + B² true?

A. Always
B. Never
C. If A = B
D. If AB = BA

Answer: D) If AB = BA

Explanation: Expanding (A + B)² gives (A + B)(A + B) = A² + AB + BA + B². For this to equal A² + 2AB + B², we must have AB = BA (the matrices commute).

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