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If `A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]]`, prove that `A^n=[[3^(n-1), 3^(n-1) , 3^(n-1)],[ 3^(n-1), 3^(n-1) , 3^(n-1)],[ 3^(n-1) , 3^(n-1), 3^(n-1)]]` `n in N`.

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V PUBLICATION-MATRICES-QUESTION BANK
  1. If A and B are symmetric matrices of the same order, then show that A ...

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  2. Let A=[[2 , -1],[3 , 4]], B=[[5, 2],[ 7, 4]] , C=[[2, 5],[ 3, 8]...

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  3. If A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]], prove that A^n=[[3^(n-...

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  4. if A=[[3, -4],[ 1, (-1)]], then prove that A^n=[[1+2 n, -4 n ],[n...

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  5. If A and B are symmetric matrices, prove that A B-B A is a skew symmet...

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  6. Show that the matrix B^' A B is symmetric or skew symmetric according ...

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  7. Find the values of x, y, z, if the matrix A=[[0, 2 y, z],[ x, y, ...

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  8. For what values of x:[[1, 2, 1]] [[1, 2, 0],[ 2, 0, 1],[ 1, 0...

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  9. If A=[[3,1],[-1,2]] then Hence show that A^2-5A+7I=0

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  10. Find x, if [[x,-5,-1]] [[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]][[x],[...

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  11. Find the matrix X so that X[[1 , 2, 3],[ 4, 5, 6]]=[[-7, -8, -9]...

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  12. If A and B are square matrices of the same order such that A B=B A,the...

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  13. If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I, then A) ...

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  14. If the matrix A is both symmetric and skew symmetric, then: A)A is a d...

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

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  16. Construct a m xx n matrix A=[[a(ij)]] whose elements a(ij) is given by...

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  17. If [[a+b ,2],[ 5 , a b]]=[[6 , 2],[ 5, 8]], find the values of a an...

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  18. Complete the following product [[1 , 0 , -5],[ 2, 0, 4]][[3 , 1],[ ...

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  19. Find the product [[2],[ -1],[ 3]][[1 , 3 ,6]]

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  20. If omega is a complex cube root of unity, show that [[1 , omega, ome...

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