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A square non-singular matrix A satisfies...

A square non-singular matrix A satisfies `A^2-A+2I=0," then "A^(-1)`=

A

`I-A`

B

`1/2(I-A)`

C

`I+A`

D

`1/2(I+A)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`A^2-A +2I =0` ltbRgt `rArr A-A^2=2I`
`A(I-A)rArr A{1/2(I-A)}=IrArrA^(-1)=1/2(I-A)`
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OBJECTIVE RD SHARMA-MATRICES-Chapter Test
  1. A square non-singular matrix A satisfies A^2-A+2I=0," then "A^(-1)=

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  2. If A is an invertible matrix and B is a matrix, then

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  3. What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c)...

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  4. If {:A=[(a,0,0),(0,b,0),(0,0,c)]:}," then "A^(-1), is

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  5. The inverse of the matrix {:[(1,3),(3,10)]:} is equal to

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  6. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

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  7. If {:X=[(3,-4),(1,-1)]:}, the value of X^n is equal to

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  8. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

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  9. For the system of equaltions : x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

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

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  11. if |[4,x+2],[2x-3,x+1]| is a symmetric then x=

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  12. If {:A+B=[(1,0),(1,1)]andA-2B=[(-1,1),(0,-1)]:}," then "A=

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  13. {:[(-6,5),(-7,6)]^(-1)=:}

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  14. From the matrix equation AB = AC we can conclude B = C provided that

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  15. If I3 is the identily matrix of order 3, then (I3)^(-1)=

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  16. Let a, b, c be positive real numbers. The following system of equation...

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  17. If A and B are two matrices such that A+B and AB are both defind, then

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  18. A and B are tow square matrices of same order and A' denotes the tran...

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  19. Consider the system of equations a1x+b1y+c1z=0 a2x+b2y+c2z=0 a3...

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  20. The system of linear equations x+y+z=2 2x+y-z=3 3x+2y+kz=4 has a...

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  21. If A and B are square matrices of order 3 such that absA=-1,absB=3," t...

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