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If A is a square matrix such that A^2=...

If `A` is a square matrix such that `A^2=I` , then find the simplified value of `(A-I)^3+(A+I)^3-7A` .

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Let A ,\ B be two matrices such that they commute. Show that for an...

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  2. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+I .

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  3. If A is a square matrix such that A^2=I , then find the simplified...

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  4. If A=[3\ \ \ 5] , B=[7\ \ \ 3] , then find a non-zero matrix C such...

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  5. Compute the indicated products: [a b-b a][a-bb a] (ii) [1-2 2 3][1 ...

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  6. Show that A B!=B A in the following case: A=[5-1 6 7] and B=[2 1 3 ...

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  7. Compute the products A B and B A whichever exists in each of the fol...

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  8. Compute the products A B and B A whichever exists in each of the fol...

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  9. Show that A B!=B A in each of the following cases: A=[[1, 3,-1],[2,-...

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  10. Evaluate the following: ([(1,3),( -1,-4))]+[(3 ,-2 ),(-1 ,1)])[(1 ,3,5...

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  11. If A=[[1, 0],[ 0, 1]] , B=[[1,0],[0,-1]] and C=[[0, 1],[ 1, 0]] , then...

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  12. If A=[[2,-1],[ 3, 2]] and B=[[0, 4],[-1, 7]] , find 3A^2-2B+I .

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  13. If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

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  14. If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(...

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  15. If A=[(ab ,b^2) ,(-a^2 ,-ab)] , show that A^2=O .

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  16. If A=[cos2thetasin2theta-sin2thetacos2theta] , find A^2 .

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  17. If A=[(2 ,-3, -5), (-1, 4, 5),( 1, -3 ,-4)] and B=[(-1, 3, 5), (1,-3, ...

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  18. If A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]] and B=[[a^2, ab, ac],[ ab, ...

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  19. If A=[(2, -3, -5) , (-1, 4, 5), (1, -3, -4)] and B=[(2, -2, -4) , (-1,...

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  20. Let A=[(-1 ,1,-1),(3,-3 ,3),( 5, 5, 5)] and B=[(0 ,4 ,3 ),(1,-3,-3),(-...

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