Select and write the most appropriate answer from the given alternatives in each of the following :
The inverse of the matrix `{:((-1,5),(-3,2)):}` is

Options

A. `(1)/(13)[{:(2,-5),(3,-1):}]`
B. `(1)/(13)[{:(-1,5),(-3,2):}]`
C. `(1)/(13)[{:(-1,-3),(5,2):}]`
D. `(1)/(13)[{:(1,5),(3,-2):}]`

Explanation

`A=[{:(a,b),(c,d):}]`
`A^(-1)=(1)/(ad-bc)=[{:(d,-b),(-c,a):}]`
So, `[{:(1-,5),(-3,2):}],=(1)/(-2-(-15))[{:(2,-5),(3,-1):}]`
`=(1)/(13)[{:(2-,5),(3,-1):}]`
Hence, correct answer from the given alternative is (a)