11.9.6 Inverse of a matrix in ℤ/pℤ
In Xcas mode, Inverse is simply the inert form of
inverse; namely, it gives the inverse of a matrix without
evaluating it. (See Section 15.1.2.)
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.
-
In Maple mode, Inverse takes
A, a matrix with elements in ℤ/pℤ.
- Inverse(A) returns the inverse of A.
Example
Input in Xcas mode:
| Inverse([[1,2,9] mod 13,[3,10,0] mod 13,[3,11,1] mod13]) |
|
| |
inverse | ⎛
⎜
⎜
⎜
⎜
⎜
⎝ |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎣ | | 1%13 | 2%13 | |
| 3%13 | | 0%13 |
| 3%13 | | 1%13
|
| ⎤
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| ⎞
⎟
⎟
⎟
⎟
⎟
⎠ |
| | | | | | | | | | |
|
To get the actual inverse, enter:
|
| |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎣ | | ⎤
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| | | | | | | | | | |
|
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 |