5.49.1 Recognize an isometry : isom
isom takes as argument the matrix of a linear
function in dimension 2 or 3.
isom returns :

if the linear function is a direct isometry,
the list of the characteristic elements of this isometry and +1,
 if the linear function is an indirect isometry,
the list of the characteristic elements of this isometry and 1
 if the linear function is not an isometry,
[0].
Input :
isom([[0,0,1],[0,1,0],[1,0,0]])
Output :
[[1,0,1],1]
which means that this isometry is a 3d symmetry with respect to the plane
x − z = 0.
Input :
isom(sqrt(2)/2*[[1,1],[1,1]])
Output :
[pi/4,1]
Hence, this isometry is a 2d rotation of angle
π/4.
Input :
isom([[0,0,1],[0,1,0],[0,0,1]])
Output :
[0]
therefore this transformation is not an isometry.