Question

for any two square matrices of same order is it true that (a+b)^2=a^2+2ab+b^2? justify your answer?​

Answer 1

For any two square matrices of the same order, it is not true every time that (a+b)^2=a^2+2ab+b^2.

• Note: If two matrices A and B satisfy the criteria AB = BA, then they are said to commute.  
• The given condition is true only when matrices A and B will commute with each other.
• Considering the matrices A and B, we have,
• (A + B)² = (A + B) (A + B)
• (A + B)² = A² + AB + BA + B²
• if AB = BA (commute) then,  
• (A+B)² = A² + 2AB + B².
• The condition is satisfied.

Answer 2

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