path traversal of a matrix

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Given matrix ,wanted to find all path traversal in c# OR any language
SUppose there is 4*4 matrix,
then if starting vertex is at point [0][0] then it can traverse to [0][1],[1][0],[1][1] all its adjacent but no vertex in a path can visit twice.
if from [0][0] it traverse to [1][1] further adjacent vertex where it can travel to are [0][0],[1][0],[2][0],[0][1],[2][1],[0][2],[1][2],[2][2] but it cannot traverse to [0][0] as it is already visited in particular path.
I want all such posible path which traverse all vertex from start of any vertex.