If A is non-singular and (A-2I)(A-4I)=0 ...

If `A` is non-singular and `(A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1)` is equal to a.`0I ` b. `2I` c. `6I` d. `I`

A

`O`

B

`I`

C

`2I`

D

`6I`

Text Solution

Verified by Experts

The correct Answer is:

B

we have, `(A-2I) (A-4I) = 0`
`rArr A^(2) - 4A - 2 A + 8 I^(2) = 0`
`rArr A^(2) - 6 A+ 8 I =0`
`rArr A^(-1) (A^(2)-6A=8I) = A^(-1)0`
` rArr A- 6 I + 8 A^(-1) = 0`
`rArr 1/6 A + 4/3 A^(-1) = I`

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