Select and write the most appropriate answer from the given alternatives in each of the following :
If `A^(-1) = 1/3 {:((1,4,-2),(-2,-5,4),(1,-2,1)):} and |A| = 3`,
then (adj A) = …

Options

A. `(1)/(9)[{:(1,4,-2),(-2,-5,4),(1,-2,1):}]`
B. `[{:(1,2,1),(4,-5,-2),(-2,4,4):}]`
C. `[{:(1,4,-2),(-2,-5,4),(1,-2,1):}]`
D. `[{:(-1,-4,2),(2,5,-4),(1,-2,1):}]`

Answer

C

Explanation

Given, `A^(-1)=(1)/(3)[{:(1,4,-2),(-2,-5,4),(1,-2,1):}]and|A|=3`
We know that , `A^(-1)=(1)/(|A|)(adj.A)`
`therefore.A=|A|*A^(-1)`
`=(3)/(3)[{:(1,4,-2),(-2,-5,4),(1,-2,1):}]`
`=[{:(1,4,-2),(-2,-5,4),(1,-2,1):}]`
Hence ,the correct answer from the given alternative is