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

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

A

There cannot exist any B such that AB = BA

B

There exist more than one but finite number of B's such that AB = BA

C

There exists exactly one B such that AB = BA

D

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

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The correct Answer is:
D
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AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES -PRACTICE EXERCISE
  1. If A is a symmetric matrix and n epsilon N, then A^(n) is

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  2. If A=[(0,1),(1,0)] then A^(2004)=

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  3. If A=[(1,3),(3,4)] and A^(2)-kA-5I(2)=O then k=

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  4. If the matrix A=((1,-1),(-1,1)) then A^(n+1)=

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  5. [(2,-1),(3,-2)]^(n)=[(1,0),(0,1)] if n is

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  6. If A=[(1,1),(1,1)] and ninN then A^(n)=

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  7. IF A=[{:(costheta,sintheta),(-sintheta,costheta):}] then show that for...

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  8. If A=[(0,a+1,b-2),(2a-1,0,c-2),(2b+1,2+x,0)] is skew symmetric then a+...

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  9. If A is a skew symmetric matrix and n is an even positive integer then...

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  10. A=[a(ij)](3xx3) is a square matrix so that a(ij)=i^(2)-j^(2) then A is...

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  11. A is a symmetric matrix or skew symmetric matrix. Then A^(2)is

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  12. If A="diag "["1 -1 2"],B=" diag "["2 3 -1"] and 3A+4B = diag [...

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  13. Observe the following lists and matching from List - I to List - II is...

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  14. If A=[(a,b),(b,a)] and A^(2)=[(alpha, beta),(beta, alpha)] then

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

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

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  17. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  18. If A=[(5a,-b),(3,2)] and A. adjA = A.A^(T) then 5a+b is equal to

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  19. Let A be 3xx3 matrix such A^(2)-5A+7I=0 statement 1 : A^(-1)=(1)/(7)(5...

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  20. A=[(-4,-1),(3,1)] then the determinant of the matrix (A^(2016)-2.A^(2-...

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