Select and write the most appropriate answer from the given alternatives in each of the following :
The inverse of the matrix `{:((1,-1),(2,3)):}` is

Options

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

Explanation

Let `A = [{:(1,-1),(2,3):}]`
`|A| = 3-(-2) = 5`
Cofactors of A, `a_(11) = 3,a_(12) = - 2`
`a_(21) = 1,a_(22) = 1`
So, matrix of cofactor = `[{:(3,-2),(1,1):}]`
`A^(-1) =(1)/(|A|)adj A`
` = (1)/(5)[{:(3,-2),(1,1):}]`
`A^(-1) = (1)/(5) [{:(3,1),(-2,1):}]`
Hence, the corrct answer from the given alternativeis (b)