Assertion (A): For square matrices $A$ and $B$ of the same order, $(A + B)^2 = A^2 + 2AB + B^2$ need not hold.
Reason (R): $(A + B)^2 = A^2 + AB + BA + B^2$ , and $AB$ need not equal $BA$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Expanding $(A + B)(A + B)$ keeps the order of each product: $A^2 + AB + BA + B^2$ .
This becomes $A^2 + 2AB + B^2$ only when $AB = BA$ , so R is true and explains A.

Concept: Algebraic identities and matrices
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsProperties of multiplication, and powers

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Ten questions from Matrices, at your own pace.

Assertion (A): For square matrices AAA and BBB of the same order, (A+B)2=A2+2AB+B2(A + B)^2 = A^2 + 2AB + B^2(A+B)2=A2+2AB+B2 need not hold.Reason (R): (A+B)2=A2+AB+BA+B2(A + B)^2 = A^2 + AB + BA + B^2(A+B)2=A2+AB+BA+B2, and ABABAB need not equal BABABA.

Explanation

Assertion (A): For square matrices $A$ and $B$ of the same order, $(A + B)^2 = A^2 + 2AB + B^2$ need not hold.
Reason (R): $(A + B)^2 = A^2 + AB + BA + B^2$ , and $AB$ need not equal $BA$ .