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

Options

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