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Let A and B two symmetric matrices of or...

Let A and B two symmetric matrices of order 3.
Statement 1 : `A(BA)` and `(AB)A` are symmetric matrices.
Statement 2 : `AB` is symmetric matrix if matrix multiplication of A with B is commutative.

A

Statement 1 is false, statement 2 is true.

B

Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1.

C

Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1.

D

Statement 1 is true, statement 2 is false.

Text Solution

Verified by Experts

The correct Answer is:
C
`(A(BA))^(T)=(BA)^(T) A^(T)`
`=(A^(T) B^(T)).A^(T)`
`=(AB) A`
`=A(BA)`
Similarly `((AB)A)^(T)=(AB)A`
Clearly both statements are true but statement 2 is not a correct explanation of statement 1.
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