Question

If `A` is non-singular and `(A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1)` is equal to `O I` b. `2I` c. `6I` d. `I`
A. I
B. O
C. 2I
D. 6I

Answer 1

Correct Answer - A
We have,
`(A-2I)(A-4I)=O`
`rArr A^2-2A-4A+8I=O`
`rArr A^2-6A+8I=O`
`rArr A^(-1) (A^2-6A+8I)=A^9-1)O`
`rArr A-6I+8A^(-1)=O`
`rArr A+8A^(-1)=6IrArr 1/6A +4/3A^(-1)=I`