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I have to do this often, so I wrote a function:

def matrix_full_simplify(mat,m,n):
    matsimp=mat;
    for i in range(m):
        for j in range(n):
             matsimp[i,j]=mat[i,j].full_simplify();
    return matsimp;

Use:

amat = matrix_full_simplify(amat)

You could easily adapt this to be better or require fewer arguments and can create a similar function for vectors.