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Mathematics

A, B and C are square matrices of order 2 such that AB = C.

Assertion (A): BA = C

Reason (R): Matrix multiplication is not always commutative.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Matrices

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Answer

Given, A, B and C are square matrices of order 2 such that AB = C.

Matrix multiplication is not always commutative.

So, reason (R) is true.

⇒ AB ≠ BA

So, BA is not necessarily equal to C.

So, assertion (A) is false.

Thus, Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.

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