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Let A =((1,2),(3,4))and B= ((a,0),(0,b))...

Let `A =((1,2),(3,4))and B= ((a,0),(0,b)), a, bin N.` Then,

A

There exists more than one but finite number of B’s such that AB=BA

B

There exists exactly one B such that

C

There exist infinitely many B’s such that AB=BA

D

There cannot exist any B such that

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  2. If A and B f are square matrices of size nxxn such that A^(2) - B^(2...

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  3. Let A =((1,2),(3,4))and B= ((a,0),(0,b)), a, bin N. Then,

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  4. If A is a square matrix such that A^2-A+l=0, then the inverse of A is

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  5. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  6. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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  7. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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  8. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

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  9. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

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  10. If the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4cy...

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  11. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

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  12. If omega is a non-real cube root of unity and n is not a multiple o...

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  13. if a,b,c are positive and are the pth qth and rth terms respectively ...

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  14. If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(...

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  15. If A is a symmetric matrix and B is a skew-symmetric matrix such that ...

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  16. The total number of matrices A = [{:(0, 2y, 1), (2x, y, -1), (2x, -y,...

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  17. Let A={:(cosalpha,-sinalpha),(sinalpha,cosalpha):},(ainR) such that A...

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  18. Let P=[(1, 0, 0),(3, 1, 0),(9, 3, 1)]Q=[q(ij)] and Q=P^5+I3 then (q21+...

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  19. Let A = ((0,2q,r),(p,q,-r),(p,-q,r)). If A A^(T) = I(3), then |p| is

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  20. The value of theta lying between 0 and pi/2 and satisfying the equatio...

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