Assertion (A): If $A \ne O$ and $AB = AC$ , it need not follow that $B = C$ .
Reason (R): A product of two non-zero matrices can be the zero matrix.

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

$AB = AC$ means $A(B - C) = O$ . With $A \ne O$ , that can still happen while $B - C \ne O$ , because two non-zero matrices can multiply to $O$ .
So R is true and is the reason A is true.

Concept: Cancellation fails for matrices
Typical timeTypical: 90 s
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The rule this testsProperties of multiplication, and powers

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Assertion (A): If A≠OA \ne OA=O and AB=ACAB = ACAB=AC, it need not follow that B=CB = CB=C.Reason (R): A product of two non-zero matrices can be the zero matrix.

Explanation

Assertion (A): If $A \ne O$ and $AB = AC$ , it need not follow that $B = C$ .
Reason (R): A product of two non-zero matrices can be the zero matrix.