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If A and B are square matrices of same o...

If A and B are square matrices of same order then `(A^(-1)BA)^(n)`= ………… , `n inN`.

A

`A^(-n)B^(n)A^(n)`

B

`A^(n)B^(n)A^(-n)`

C

`A^(-1)B^(n)A`

D

`n(A^(-1)BA)`

Text Solution

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The correct Answer is:
C
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KUMAR PRAKASHAN-MATRICES -TEXTBOOK BASED MCQS
  1. If AB=AandBA=B then A^(2)+B^(2)= ………..

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  2. If A is any square matrix then AA' is a ………. Matrix.

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  3. If A and B are square matrices of same order then (A^(-1)BA)^(n)= ………...

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  4. A=[{:(0,1,2),(1,2,3),(3,a,1):}]and A^(-1)=[{:(1/2,-1/2,1/2),(-4,3,c),(...

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  5. [{:((1)/(25),0),(x,(1)/(25)):}]=[{:(5,0),(-a,5):}]^(-2) then x =………..

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  6. [1" "x" "1][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(x):}]=0 then x=……...

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  7. A is a 3xx4 matrix .A matrix B is such that A'B and BA' are defined . ...

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  8. P is a 2xx2 matrix . P'=P^(-1) then P=……..

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  9. A is a 3xx3 matrix , then |3A|=....|A|.

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  10. If A=[a(ij)](nxxn) such that a(ij)=0, for i nej then , A is …….. (a(...

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  11. A=[{:(0,0,-1),(0,-1,0),(-1,0,0):}],the correct statement is ......

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  12. If A is skew -symmetric 3xx3 matrix , |A| =……..

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  13. The system of equations ax+y+z=a-1,x+ay+z=a-1andx+y+az=a-1 does not h...

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  14. If A=[{:(a,b),(b,a):}]andA^(2)=[{:(x,y),(y,x):}] then , x=……, y=…….

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  15. If alphaandbeta are not the multiple of (pi)/(2)and [{:(cos^(2)alpha,c...

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  16. If [{:(x,0),(1,y):}]-[{:(2,-4),(-3,-4):}]=[{:(3,5),(6,3):}]-[{:(2,1),(...

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  17. If inverse of A=[{:(1,-1,1),(2,1,-3),(1,1,1):}]is (1)/(10)[{:(4,2,2),(...

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  18. If AB=BAandA=[{:(1,1),(0,1):}]then, B=......

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  19. If A=[{:(1,3),(3,4):}]andA^(2)=kA=5I=O,then k =....

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  20. If [1" "x" "1][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(x):}]=O, then x...

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