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Let A and B be two nonsingular square ma...

Let A and B be two nonsingular square matrices, `A^(T)` and `B^(T)` are the tranpose matrices of A and B, respectively, then which of the following are correct ?

A

`B^TAB` is symmetric matrix if A is symmetric

B

`B^T AB` is symmetric matrix if B is symmetric

C

`B^TAB` is skew-symmetric matrix for every matrix A

D

`B^TAB` is skew-symmetric matrix If A is skew-symmetric

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The correct Answer is:
A, D
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -LEVEL 2
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  7. If P is a 3xx3 matrix such that P^(T) = 2 P + I , where P^(T) is the...

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  8. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

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  17. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

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