function matrix

[scidam]

shouldn't the symmetric case be [[a,d,g],[b,e,h],[c,f,i]] ?
and the skew be [[-a,-d,-g],[-b,-e,-h],[-c,-f,-i]] ?

Everything depends on values of variables a, b, ..., i. I think, it would be better to define symmetric, skew and arbitrary matrices directly, without using variables, e.g.:

symmetric_A = [[1, 2, 3],
               [2, 10, 15],
               [3, 15, 1000]]

skew_A =       [[0, 2, 3],
               [-2, 0, 15],
               [-3, -15, 0]]

#Skewness means that A = -A.T, so main diagonal of a skew matrix always consist of zero values.

arbitrary_A [[1,2,3],
             [4,5,6],
             [7,8,9]]