Determinant of a matrix in $\mathbb {Z}$/p$\mathbb {Z}$ : det

det takes as argument a matrix A with coefficients in Z/pZ.
det returns the determinant of this matrix A.
Computation are done in $\mathbb {Z}$/p$\mathbb {Z}$ by Gauss reduction. Input :

det([[1,2,9]%13,[3,10,0]%13,[3,11,1]%13])

Or :

det([[1,2,9],[3,10,0],[3,11,1]]%13)

Output :

5%13

hence, in $\mathbb {Z}$/13$\mathbb {Z}$, the determinant of A = [[1, 2, 9],[3, 10, 0],[3, 11, 1]] is 5%13 (in $\mathbb {Z}$, det(A)=31).