WA in SEAGRP

Problem: https://www.codechef.com/problems/SEAGRP
My WA solution: https://www.codechef.com/viewsolution/34845682
If the determinant of Tutte matrix is zero, then matching is impossible. Using this fact I have tried to solve this question. If there exists an edge between i and j, I put random value in a[i][j], and put a[j][i]= -a[i][j] (a is the matrix).
Is there something wrong with my logic itself? It may be possible that using random values still gives the determinant zero that’s why I find the determinant multiple times.

i am a little confused with contradictory statement and example test case 3.

they said in input section that graph will not contain cycles.

and test case 3 is simple square with all 4 nodes connecting to all 3 other nodes…

Where is that mentioned? I don’t see. Are you referring to “loops”?

yes loops.

By loops here I think they mean edges that connect a vertex to itself, not cycles.