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If A={:[(2,2),(1,-2)]:}," and "A^(-1)=al...

If `A={:[(2,2),(1,-2)]:}," and "A^(-1)=alphaA," then " alpha=`

A

7

B

-7

C

`(1)/(7)`

D

`-(1)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
C
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MARVEL PUBLICATION-MATRICES-TEST YOUR GRASP
  1. If A={:[(2,2),(1,-2)]:}," and "A^(-1)=alphaA," then " alpha=

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  2. If A=[a(ij)](2xx2)" where "a(ij)=2i+j," then :"A=

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  3. If A+3B={:[(1,2,3),(-2,3,5)]:}" and "2A+3B={:[(2,-1,4),(-1,5,2)]:}," t...

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  4. If A and B are square matrices of order 3 such that det(A)=-2 and det(...

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  5. If A is a non-singularmatrix such that A^(2)-A+I=O," then: "A^(-1)=

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  6. If A=[(x,1),(1,0)] and A=A^(-1), then x= . . . .

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  7. If AC=A" and "BA=B," then: "A^(2)=

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  8. For a invertible matrix A if A(adjA)=[(10,0),(0,10)], then |A|=

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  9. If A and B are square matrices of the same order such that A^(2)=A,B^(...

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  10. If A={:[(2,3),(1,-1)]:}" and "A^(2)=A+B," then : "B=

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  11. Solve system of linear equations, using matrix method, x y" "+" "2...

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  12. If A={:[(1,2),(3,4)]:}," then: " adj(adjA)=

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  13. If A={:[(4,2),(5,3)]:}" then :"|adj(adjA)|=

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  14. If A={:[(2,-1,1),(1,2,1),(-1,1,3)]:}" then "|adj(adjA)|=

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  15. If A={:[(secx,tanx),(tanx,secx)]:}" and "A(adj*A)=k{:[(1,0),(0,1)]:},"...

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  16. If A=[[0,1] , [-1,0]]=(alphaI+betaA)^2 then alpha and beta =

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  17. If A={:[(2,1),(3,2)]:}" and "B={:[(1,2),(-1,3)]:}," then: "B^(-1)A=

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  18. If A={:[(2,3),(1,2)]:}" and "B={:[(3,1),(1,0)]:}," then: "B^(-1)A^(-1)...

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  19. If square matrices A and B are such that A^(2)=A,B^(2)=B and A,B commu...

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  20. If A=[a(ij)](3xx3) is a scalar matrix such that a(ij)=5" for all "i=j,...

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  21. If A={:[(1,a),(0,1)]:}," then, for all "ninN," matrix "A^(n)=

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