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If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (...

If `[(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0),(0,1)],` then the least positive integral value of `k`, is

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

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  2. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

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  3. If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0)...

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  4. If the matrix A B is zero, then It is not necessary that either A=O...

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  5. Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , then A^n is equal to [(a^n,0,...

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  6. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

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  7. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

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  8. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals (a)[(1,n a),(0, ...

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  9. If A=[[1, 2, x], [0 ,1 ,0],[ 0, 0, 1]] and B=[[1,-2,y],[0, 1, 0 ],[0...

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  10. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

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  11. If A=[alphabetagamma-alpha] is such that A^2=I , then 1+alpha^2+betaga...

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  12. If S=[S(i j)] is a scalar matrix such that s(i i)=ka n dA is a square ...

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  13. If a square matrix such that A^2=A , then (I+A)^3-7A is equal to A ...

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  14. If a matrix A is both symmetric and skew-symmetric, then A is a dia...

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  15. The matrix [(0, 5,-7),(-5, 0, 11),( 7,-11, 0)] is (a) a skew-symmetr...

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  16. If A is a square matrix, then A A is a (a) skew-symmetric matrix (b)...

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  17. If A and B are symmetric matrices, then A B A is (a) symmetric m...

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  18. If A=[(5,x),( y,0)] and A=A^T , then a) x=0,\ \ y=5 (b) x+y=5 (c)...

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  19. If A is 3xx4 matrix and B is a matrix such that A^T B and B A^T are bo...

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  20. If A=[a(i j)] is a square matrix of even order such that a(i j)=i^2-...

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