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If A and B are two square matrices of the same size, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ can hold if and only if

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AB = BA

AB + BA = O

|AB| ≠ 0

|AB| = 0

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detailed solution

Correct option is A

(A+B)2=(A+B)(A+B)=A2+BA+AB+B2∴(A+B)2=A2+2AB+B2 if and only if AB = BA

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If A and B are two square matrices of the same size, then (A+B)2=A2+2AB+B2can hold if and only if

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If A and B are two square matrices of the same size, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ can hold if and only if