Find the inverse of the matrix if it exists.

Find the inverse of the matrix if it exists.

a=[2,-5]
[1,2]

A=[2,-3]
[1,3]

A=[2,-1]
[1, 2]

The inverse of a 2x2 matrix is (1/ad-bc) x B, where
A=[a b]
[c d]
B=[d -b]
[-c a]
To get B you swap a and d, and minus b and c

For example
A=[2 -5]
[1 2]
= 1/((2 x 2) - (1 x -5)) = 1/(4+5) = 1/9
B=[2 5]
[-1 2]
So the inverse of A will be 1/9 x B
= [2/9 5/9]
[-1/9 2/9]

The ad-bc is the determinant of A, so it's really 1/detA x B

I'd imagine the inverse won't exist when detA = 0, because you can't divide by 0