Question

How do you find the inverse of `A=``((1, 3, -1), (2, 5, 1), (1, 4, -4))`?

Answer 1

The inverse of `A`, `A^-1` does not exist because the `detA=0`

Explanation:

The Inverse of `A` is `A^-1` such that `A*A^1=I`
Where I is the identity matrix with
`a_(i,j) = 1 AA-> i=j; 0` otherwise
Quickly check for the determination to check for the existence of `A^-1`
`detA = 1[(5, 1), (4, -4)] - 3[(2, 1), (1, -4)] - [(2, 5), (1, 4)]`
`detA = (-20-4) -3(-8-1)-(8-5) =0`
With `detA=0` the inverse of `A`, `A^-1` does not exist