### 5.35.5 Determinant of a matrix with coefficients in ℤ/pℤ : Det

Det is the inert form of det.
Det takes as argument a matrix with coefficients in ℤ/pℤ.
Det returns det without evaluation. It is used in conjunction with mod in Maple syntax mode to find the determinant of a matrix with coefficients in ℤ/pℤ.
Input in Xcas mode :

Det([[1,2,9] mod 13,[3,10,0] mod 13,[3,11,1] mod 13])

Output :

det([[1%13,2%13,-4%13],[3%13,-3%13,0%13], [3%13,-2%13,1%13]])

you need to eval(ans()) to get :

5%13

hence, in ℤ/13ℤ, the determinant of A=[[1, 2, 9],[3,10,0],[3,11,1]] is 5%13 (in ℤ, det(A)=31).
Input in Maple mode :

Det([[1,2,9],[3,10,0],[3,11,1]]) mod 13

Output :

5