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6.35.6  Inverse of a matrix in ℤ/pℤ: Inverse

In Xcas mode, Inverse is simply the inert form of inverse; namely, it gives the inverse of a matrix without evaluating it. (See section Section 6.47.2.) In Maple mode, the Inverse command can additionally be used in conjunction with mod to find the inverse of a matrix whose elements are in ℤ/pℤ.


Example.
Input (in Xcas mode):

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

Output:

inverse











1%132%13

−4
%13
3%13

−3
%13
0%13
3%13

−2
%13
1%13












To get the actual inverse, you can enter:
Input:

eval(ans())

Output:







2%13

−4
%13

−5
%13
2%130%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
20−5
−2−16




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