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.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
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.
Related Questions
The product AB of two matrices A and B is possible if
A and B have same number of rows.
A and B have same number of columns.
The number of columns of A is equal to the number of rows of B.
The number of rows of A is equal to the number of columns of B.
A, B and C are square matrices of order 2 such that AB = C.
Assertion (A): Product BA need not be equal to C.
Reason (R): Matrix multiplication is not associative.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).