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If B is an idempotent matrix, and A=I-B,...

If B is an idempotent matrix, and `A=I-B`, then

A

B is idempotent

B

AB = O

C

BA = O

D

None of these

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The correct Answer is:
D
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DISHA PUBLICATION-MATRICES-Exercise 2: Concept Applicator
  1. If Z is an idempotent matrix, then (I+Z)^(n)

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  2. If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...

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  3. If B is an idempotent matrix, and A=I-B, then

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  4. Let A,B and C be nxxn matrices. Which one of the following is a correc...

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  5. If A=1/pi[sin^(-1)(pix)tan^(-1)(x/pi)sin^(-1)(x/pi)cot^(-1)(pix)] and ...

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  6. Let Ad nB be 3xx3 matrtices of ral numbers, where A is symmetric, "B" ...

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  7. If P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]] and A=[[1,1] , [0,1]] and Q=PAP^...

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  8. If [(0,2b,c),(a,b,-c),(a,-b,c)] is orthogonal matrix, then the value ...

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  9. If A is a square matrix of order m, then the matrix B of same order is...

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  10. If A1, A2, , A(2n-1)a r en skew-symmetric matrices of same order, the...

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  11. For k=1/sqrt(50), the value of a, b, c such that PP' = I, where P=[(2/...

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  12. IfA^(k)= 0 (Ais nilpotent with index k), (I-A)^(p)=I+A+A^(2)+. . .+A^(...

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

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  14. If A=[(1,-1),(2,-1)] and B=[(1,a),(4,b)] and (A+B)^(2)=A^(2)+B^(2). ...

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  15. If A is a square matrix such that A A^T=I=A^TA, then A is

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  16. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

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  17. [{:(2x+y,4x),(5x-7,4x):}]=[{:(7,7y-13),(y,x+6):}] then the value of x,...

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  18. Given that [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega...

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  19. If {:A=[(alpha,0),(1,1)]andB=[(1,0),(5,1)]:}, then te value of alpha f...

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  20. [[i,0,0],[0,i,0],[0,0,i]] then A^(4n+1) =.... n in N

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