Hi. I’m trying to calculate the determinant of the following matrix and compare it with the determinant of its inverse
x = torch.tensor([[ 757.7089, -196.4800],
                   [-196.4800,   50.9489]])

x_inv = torch.inverse(x)
>tensor([[ 1092.4257,  4212.8447],
        [ 4212.8447, 16246.4883]])

I use two ways to calculate the determinant of both matrix 1-product of eigenvalues 2-torch.det()
and both ways have the problem that determinant of x is not equal to the inverse of the determinant of x_inv
print(torch.det(x)) 
>tensor(0.0466)

print(torch.det(x_inv))
> tensor(19.6592) 

And
1/0.0466  == 19.6592
> False 

which is wrong.
I even try to use
eig_val_x, _ = torch.symeig(x)
dete_x = torch.prod(eig_val_x)

eig_val_x_inv, _ = torch.symeig(x_inv)
dete_x_inv = torch.prod(eig_val_x_inv)

but still same problem exsit. and even two way of calculating determinant provide different values for the determinant.  Can some one help me with this issue.