The inverse matrix of `A=[(0,1,2),(1,2,3),(3,1,1)]` is

Options

A. `[{:((1)/(2),-(1)/(2),(1)/(2)),(-4,3,-1),((5)/(2),-(3)/(2),(1)/(2)):}]`
B. `[{:((1)/(2),-4,(5)/(2)),(1,-6,3),(1,2,-1):}]`
C. `(1)/(2)[{:(1,2,3),(3,2,1),(4,2,3):}]`
D. `(1)/(2)[{:(1,-1,-1),(-8,6,-2),(5,-3,1):}]`

Answer

A

Explanation

Let `[{:(0,1,2),(1,2,3),(3,1,1):}]`
`:. |A|=0-1(1-9)+2(1-6)`
`=8-10=-2 ne 0`
adj `A[{:(-1,1,-1),(8,-6,2),(-5,3,1):}]`
`:. A^(-1)=(adj(A))/(|A|)`
`=(1)/(2)[{:(-1,1,-1),(8,-6,2),(-5,3,-1):}]`
`=[{:(1//2,1//2,1//2),(-4,3,-1),(5//2,-3//2,1//2):}]`