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. `O`
B. `I`
C. `2I`
D. `6I`

Answer 1

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