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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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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[[i,0], [0,i]] , write A^2 .

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  2. If A=[[cosx,sinx],[-sinx,cosx]] , when A + A^T= I find x satisfying 0 ...

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  3. If A=[[cosx,-sinx],[sinx,cosx]] , find A A^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 ...

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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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