Exercise 2 solution

def cross_over_many(mat, pat, points):
    a, b = mat, pat
    for p in sorted(points):
        a, b = a[:p] + b[p:], b[:p] + a[p:]
    return a, b

mat, pat = "AAAAAAAAAA", "bbbbbbbbbb"
for points in ([4], [3, 7], [2, 5, 8], []):
    a, b = cross_over_many(mat, pat, points)
    ok = all(set(pair) == {"A", "b"} for pair in zip(a, b))
    print(points, a, b, ok)

Output:

[4] AAAAbbbbbb bbbbAAAAAA True
[3, 7] AAAbbbbAAA bbbAAAAbbb True
[2, 5, 8] AAbbbAAAbb bbAAAbbbAA True
[] AAAAAAAAAA bbbbbbbbbb True

Reading it: Each swap exchanges the tails after the point, so at every position the two results hold the two original letters between them, in one order or the other.