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If A=[(cosx,-sinx),(sinx,cosx)] , find A...

If `A=[(cosx,-sinx),(sinx,cosx)]` , find `A``A^T`

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Given: `A=[(cosx,-sinx),(sinx,cosx)]`
Then,
`A^T=[(cosx,-sinx),(sinx,cosx)]^T`

`A^T=[(cosx,sinx),(-sinx,cosx)]`

Then
`A``A^T=[(cosx,-sinx),(sinx,cosx)][(cosx,sinx),(-sinx,cosx)]`
...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[i0 0i] , write A^2 .

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  2. If A=[(cosx,sinx),(-sinx,cosx)] , find x satisfying 0<x<pi/2 when A+A^...

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  3. If A=[(cosx,-sinx),(sinx,cosx)] , find AA^T

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  4. If [(1, 0),(y,5)]+2[(x,0),( 1,-2)]=I , where I is 2xx2 unit matrix. Fi...

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  5. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

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  6. If A=[1 1 1 1] satisfies A^4=lambdaA , then write the value of lambda

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  7. If A=[-1 0 0 0-1 0 0 0-1] , find A^2 .

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  8. If A=[-1 0 0 0-1 0 0 0-1] , find A^3 .

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  9. If A=[-3 0 0-3] , find A^4 .

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  10. If [[x,2]][[3],[ 4]]=2, find x

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  11. If A=[a(i j)] is a 2xx2 matrix such that a(i j)=i+2j , write A .

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  12. Find a matrix A ,ifA+[2 3-1 4]=[3-6-3 8]

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  13. If A=[a(i j)] is a square matrix such that a(i j)=i^2-j^2 , then wr...

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  14. For any square matrix write whether AA^T is symmetric or skew-symm...

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  15. If A=[a(i j)] is a skew-symmetric matrix, then write the value of s...

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  16. If A=[a(i j)] is a skew-symmetric matrix, then write the value of s...

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  17. If A and B are symmetric matrices, then write the condition for whi...

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  18. If B is a skew-symmetric matrix, write whether the matrix A B\ A^T ...

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  19. If B is a symmetric matrix, write whether the matrix A B\ A^T is sy...

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  20. If A is a skew-symmetric and n in N such that (A^n)^T=lambda\ A^n ...

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