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If A and B are symmetric matrices of the same order and AB-BA `ne` 0 , then AB is not symmetric .

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ARIHANT PUBLICATION-MATRICES -ODISHA BUREAU .S TEXTBOOK SOLUTIONS (Exercise (b) )
  1. State which of the following matrices are symmetric , skew symmetric ...

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  2. State which of the following matrices are symmetric , skew symmetric ...

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  3. State True or False If A and B are symmetric matrices of the sam...

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  4. State'True'or'false':For any square matrix A, AA' is symmetric.

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  5. State'True'or'false':If A is any skew symmetric matrix, then A^2 is al...

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  6. State'True'or'false': If A is symmetric, then A^2,A^3,…..,A^n are all ...

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  7. State'True'or'false':If A is symmetric then A-A^1 is both symmetric an...

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  8. State'True'or'false':For any square matrix (A-A^1)^2 is skew symmetric...

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  9. State'True'or'false': A matrix which is not symmetric is skew symmetri...

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  10. If A and B are symmetric matrices of the same order with AB!= BA, fina...

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  11. If a symmetric /skew symmetric matrix is expressed as a sum of a symme...

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  12. A and B are square matrices of the same order, prove that : if A,B and...

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  13. A and B are square matrices of the same order, prove that :If A,B and ...

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  14. If [{:(1,2,0),(0,1,3),(-2,5,3):}] , then verify that A+A ' is symm...

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  15. If A=[{:(1,2,0),(0,1,3),(-2,5,3):}] then verify that A+A is symmetric ...

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  16. Prove that a unit matrix is its own inverse Is the converse true ?

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  17. If A=[{:(0,1,-1),(4,-3,3),(3,-3,4):}] show that A^(2)=I and hence A=A...

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  18. Show that [[0,1],[1,0]] is its own inverse.

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  19. Express as a sum of a symmetric and a skew symmetric matrix: [[1,2,3],...

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  20. Express as a sum of a symmetric and skew symmetric matrix. [(2,-1,3),(...

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