Question

If `A=[[2,3],[5,-2]]` then write A^-1

Answer 1

`A=[[2,3],[5,-2]]`

`therefore |A|=|[2,3],[5,-2]|=-4-15=-19ne 0`

So, A is a non-singular matrix. Therefore, it is invertible.
Now,

`C_11=−2, C_12=−5, C_21=−3, C_22=2`

`therefore adj A=[[-2,-5],[-3,2]]^T=[[-2,-3],[-5,2]]`

We know 

`A^-1 =1/|A| adjA`

`therefore A^-1=1/(-19) [[-2,-3],[-5,2]]`

`=[[2/19,3/19],[5/19,-2/19]]`