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If A^(2)-A+I=O, then A^(-1) is equal to...

If `A^(2)-A+I=O`, then `A^(-1)` is equal to

A

A

B

`A + I`

C

`I - A`

D

`A - I`

Text Solution

Verified by Experts

The correct Answer is:
C
`A^(2) -A+I=0`
` rArr I=A-A^(2) rArr I = A(I-A)`
`rArr A^(-1) I = A^(-1) (A(I-A))rArr A^(-1) =I - A`
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ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  3. If A^(2)-A+I=O, then A^(-1) is equal to

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  4. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

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  5. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

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  6. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  12. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

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  13. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  14. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  15. The number of 3xx3 matrices A whose are ether 0 or 1 and for which t...

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  16. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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