### 5.33.6 Inverse of a matrix in ℤ/pℤ : Inverse

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

Inverse([[1,2,9] mod 13,[3,10,0] mod 13,[3,11,1] mod13])

Output :

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

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

[[2%13,-4%13,-5%13],[2%13,0%13,-5%13], [-2%13,-1%13,6%13]]

which is the inverse of A=[[1,2,9],[3,10,0],[3,11,1]] in ℤ/13ℤ.
Input in Maple mode :

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

Output :

[[2,-4,-5],[2,0,-5],[-2,-1,6]]