travelling salesmen problem advice with matrix

I have come to one last final struggle in my traveling salesmen problem that i have been working on, i have generated a 10 by 10 matrix (the one attached).

i have gotten to the point were i now do not know how to structure my matrix into a answer to say what the shortest distance is or how to calculate that distance, any help advice would be appreciated.

i have been pointed in the direction of perms but permutating a single line would be pointless because it will only rearrange the choices of 'a' to a all places it can go which doesn't seem logical

[Walter Roberson]

duplicated by later http://www.mathworks.co.uk/matlabcentral/answers/89353-find-the-smallest-route