Select and write the most appropriate answer from the given alternatives in each of the following :
The inverse of the matrix `{:((2,0,0),(0,1,0),(0,0,-1)):}` is

Options

A. `[((1)/(2),0,0),(0,1,0),(0,0,-1)]`
B. `[(-(1)/(2),0,0),(0,-1,0),(0,0,1)]`
C. `[(-1,0,0),(0,-(1)/(2),0),(0,0,(1)/(2))]`
D. `-(1)/(2)[(-(1)/(2),0,0),(0,-1,0),(0,0,-1)]`

Answer

A

Explanation

Let `A=[(2,2,0),(0,1,0),(0,0,-1)]`
`therefore" "|A|=2(-1-0)-0+0=-2 ne 0`
`therefore" "A^(-1)` exists.
Consider`" "A A^(-1)=1`
`therefore" "[(2,0,0),(0,1,0),(0,0,-1)]A^(-1)=[(1,0,0),(0,1,0),(0,0,1)]`
Applying `R_(1) rarr (1)/(2)R_(1) and R_(3) rarr -R_(3)`, we get
`[(1,0,0),(0,1,0),(0,0,1)]A^(-1)=[(1//2,0,0),(0,1,0),(0,0,-1)]`
`A^(-1)[(1//2,0,0),(0,1,0),(0,0,-1)]`