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If A=[(ab,b^(2)),(-a^(2),-ab)] then A is...

If `A=[(ab,b^(2)),(-a^(2),-ab)]` then A is

A

idempotent matrix

B

involutory matrix

C

nilpotent matrix of index 2

D

nilpotent matrix of index 3

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The correct Answer is:
C
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AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES -EXERCISE - I
  1. If tr(A)=3,tr(B)=5 then tr(AB)=

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  2. If A=[(4,x+2),(2x-3,x+1)] is symmetric then trace of A is

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  3. If A=[(x,1,4),(-1,0,7),(-4,-7,0)] such that A'=-A then x=

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  4. P+Q=((2,3,5),(4,1,2),(1,2,1)),P is symmetric, Q is a skew symmetric ma...

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  5. If 3A+4B'=[(7,-10,17),(0,6,31)],2B-3A'=[(-1,18),(4,-6),(-5,-7)] then B...

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  6. If A=[(cos theta, sin theta, 0),(-sin theta, cos theta, 0),(0,0,1)] th...

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  7. If 3A=[(-1,2,2),(2,-1,2),(2,2,-1)] then

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  8. If A=[(2,x-3,x-2),(3,-2,-1),(4,-1,-5)] is a symmetric matrix then x =

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  9. If A=[(ab,b^(2)),(-a^(2),-ab)] then A is

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  10. If A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] then A is

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  11. If A=[a(ij)](nxxn) and a(ij)="A.M." of {i,j} then A is

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  12. If the order of A is 4xx3, the order of B is 4xx5 and the order of C i...

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  13. If A is a 3xx4 matrix and B is matrix such that A^(T)Band BA^(T) are b...

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  14. If A is idempotent matrix A+B=I then B is

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  15. If A is a square matrix then A-A^(T) is a . . . . . .. Matrix

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  16. If A, B are symmetric matrices of the same order then show that AB-BA ...

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  17. A square matrix (a(ij)) where a(ij)=0 for i!=j and a(ij)=k (constant) ...

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  18. If a matrix A is both symmetric and skew symmetric then A is

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  19. If B an idempotent matrix and A=I-B then AB =

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  20. Statement I : Trace of matrix is defined for square matrices only. S...

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