### Polynomials over Quaternions via Determinants

I currently trying to get polynomials over quaternions out of determinants of matrices. Example giving below:

Q.<i,j,k> = QuaternionAlgebra(SR, -1, -1)

A=matrix(4,4,[0,j,0,j,j,0,0,j,0,0,0,0,j,j,0,0])

I=matrix.identity(4)

P=(j*A-x*I)

P.det()

But it doesn't work. Any idea?