Define the indices that you want to interchange in a list $ind$ and then you can index into the array $a$ directly.
a = {{1, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {4, 5, 6, 7, 8}, {5, 6, 7, 8, 9}}; ind = {1, 3, 4, 2, 5}; a[[ind, ind]] bill s
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