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If f(alpha)=[[cosalpha,-sinalpha,0],[sin...

If `f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n` prove that `[F(alpha)]^(-1)=F(-alpha)dot`

A

`F(-alpha)`

B

`F(alpha^(-1))`

C

`F(2alpha)`

D

none of these

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A
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...

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  2. If A=[a(ij)] is a scalar matrix of order nxxn and k is a scalar, then ...

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  3. If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],...

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  4. If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0...

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  5. Find the matrix A satisfying the matrix equation [{:(2,1),(3,2):}]A[...

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  6. If [(1,-tantheta),(tantheta,1)][(1,tantheta),(-tantheta,1)]^(-1)=[(a,-...

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  7. If A and B are two matrices such that A+B and AB are both defind, then

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  8. If a matrix A is such that 3\ A^3+2\ A^2+5\ A+I=0 , then A^(-1) is equ...

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  9. Let A and B be matrices of order 3 xx 3. If AB = 0, then which of the ...

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  10. If A is an invertible matrix, then which of the following is correct

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  11. Which of the following is/are incorrect? (i) adjoint of a symmetri...

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  12. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

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  13. If for matrix A,A^(2)+l=0, where l is the identity matrix, then A equa...

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  14. If A=[a(ij)](mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemi...

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  15. If In is the identity matrix of order n, then rank of In is

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  16. A=[a(ij)](mxxn) is a square matrix, if

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  17. The rank of a null matrix is

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  18. If A is a matrix such that there exists a square submatrix of order r ...

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  19. Which of the following is correct ?

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  20. If a square matrix A is orthogonal as well as symmetric, then

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