Given that A and B are square matrices of the same order.We need to check if (A + B)2 = A2 + 2AB + B2.We know (A + B)2 = (A + B)(A + B)⇒ (A + B)2 = A(A + B) + B(A + B)∴ (A + B)2 = A2 + AB + BA + B2For the equation (A + B)2 = A2 + 2AB + B2 to hold, we need AB = BA that is the matrices A and B must satisfy the commutative property for multiplication.However, here it is not mentioned that AB = BA.Therefore, AB ≠ BA.Thus, (A + B)2 ≠ A2 + 2AB + B2.

Q. 663.7( 3 Votes )

Let A and B

Class 12th RD Sharma - Volume 1 5. Algebra of Matrices

Answer :

Given that A and B are square matrices of the same order.

We need to check if (A + B)² = A² + 2AB + B².

We know (A + B)² = (A + B)(A + B)

⇒ (A + B)² = A(A + B) + B(A + B)

∴ (A + B)² = A² + AB + BA + B²

For the equation (A + B)² = A² + 2AB + B² to hold, we need AB = BA that is the matrices A and B must satisfy the commutative property for multiplication.

However, here it is not mentioned that AB = BA.

Therefore, AB ≠ BA.

Thus, (A + B)² ≠ A² + 2AB + B².

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSGive exampl NEXTIf A and B are sq

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

view all courses