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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 coorect ?

A

`B^T AB` 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^T AB` is skew-symmetric matrix if A is skew-symmetric

Text Solution

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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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  3. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

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  4. If A^(-1)=[(1,-1,2),(0,3,1),(0,0,-1//3)], then

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  5. Which of the following statements is/are true about square matrix A or...

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  6. If A, B, and C are three square matrices of the same order, then AB=AC...

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  8. Let A=[(1,0),(1,1)] . Then which of the following is not true ?

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  9. If C is skew-symmetric matrix of order n and X isnxx1 column matrix, t...

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  10. If S=[(0,1,1),(1,0,1),(1,1,0)]a n dA=[(b+c,c+a,b-c),(c-b,c+b, a-b),(b-...

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  11. If A B=A and B A=B , then show that A^2=A , B^2=B .

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  15. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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

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  18. If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsi...

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  19. If A^(-1)=[(sin^(2)alpha, 0, 0),(0, sin^(2)beta,0),(0, 0,sin^(2)gamma)...

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