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If A^5=O such that A^n != I for 1 <= n <...

If `A^5=O` such that `A^n != I` for `1 <= n <= 4`, then `(I - A)^-1` is equal to

A

`A^(4)`

B

`A^(3)`

C

`I+A`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`A^(4) (I-A) = A^(4) I - A^(5)=A^(4) - 0 = A^(4) ne I`
`A^(3) (I-A) = A^(3) I- A^(4) = A^(3) - A^(4) ne I`
`(I + A) (I-A) = I^(2) - A^(2) = I -A^(2) ne I`
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ARIHANT MATHS ENGLISH-MATRICES -Exercise (Single Option Correct Type Questions)
  1. If A^5=O such that A^n != I for 1 <= n <= 4, then (I - A)^-1 is equal ...

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  2. Let A= [[a,b,c],[p,q,r],[x,y,z]] and suppose then det (A) = 2, then d...

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  3. If A is any square matrix such that A= [ ( 2, 3) , (5,8)] then find A+...

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  4. Let a= lim (x rarr 1) (x/(lnx)-1/(xln x)), b = lim (x rarr 0) ((x^(3)-...

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  5. Let A= [[1,4],[3,2]] If theta is the angle between the two non- zero ...

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  6. If a square matrix A is involutory, then A^(2n+1) is equal to:

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  7. If A=[[cos theta,sin theta],[-sin theta,cos theta]], then lim (n rarr...

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  8. The rank of the matrix [[-1,2,5],[2,-4,a-4],[1,-2,a+1]] is (where a = ...

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  9. A is an involuntary matrix given by A=[(0,1,-1),(4,-3,4),(3,-3,4)], th...

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  10. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

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  11. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

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  12. If matrix A=[a(ij)](3xx), matrix B=[b(ij)](3xx3), where a(ij)+a(ji)=0 ...

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  13. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

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  14. If A=[[(-1+isqrt(3))/(2i),(-1-isqrt(3))/(2i)],[(1+isqrt(3))/(2i),(1-is...

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  15. The number of 2x2 matrices X satisfying the matrix equation X^2=I(Ii s...

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  16. if A and B are squares matrices such that A^(2006)=O and A B=A+B , the...

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  17. If P = [[cos frac(pi)(6), sin frac(pi)(6) ],[-sinfrac(pi)(6),cosfrac(p...

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  18. There are two possible values of A in the solution of the matrix equ...

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  19. If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos ...

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  20. In a square matrix A of order 3 the elements a(ij) 's are the sum of...

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