### 2.32.5 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 conjonction 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`