find the determinant of matrix of polynomials

I am using recursion relation to find the eigenvalues which is

 a_n (E)=([4Bn-6B-E] a_(n-2)(E) -[4B^2 ] a_(n-4) (E)+a_(n-6) (E)+g a_(n-3) (E))/(n(n-1))

To find the eigenvalues I'll have two coefficients which means I will have a matrix and I need to solve the determinant .

how can I do that ?? especially in this case when I'm working in matrix of polynomials??

 A(i,j)=(P(i,j)-Q(i,j)+R(i,j)+T(i,j))/((i-2)*(i-1));

[Karan Gill]

I assume you'll have a matrix of symbolic polynomials. Have you tried det ?

[nada al]

yes I've tried but I could not get the answer because the matrix have polynomials elements which the program consider it as not square matrix

[John D'Errico]

The determinant is not defined for a non-square matrix. You can't do magic.

[nada al]

so I was trying to find the determinant by using the coefficient a*d-b*c=0 I thought this way may work but I did not get the correct result.