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):
Output:
inverse | ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ | ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ | ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ |
To get the actual inverse, you can enter:
Input:
Output:
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
which is the inverse of A=[[1,2,9],[3,10,0],[3,11,1]] in ℤ/13ℤ.
Input (in Maple mode):
Output:
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |