def test1() -> None:
        # a^(-1)
        ainv = Matrix(3, 3, 0)
        for i in range(3):
            ainv[i, i] = 1
        print(f"a^(-1) is {ainv}")
        # u, v
        u = Matrix(3, 1, 0)
        u[0, 0], u[1, 0], u[2, 0] = 1, 2, -3
        v = Matrix(3, 1, 0)
        v[0, 0], v[1, 0], v[2, 0] = 4, -2, 5
        print(f"u is {u}")
        print(f"v is {v}")
        print(f"uv^T is {u * v.transpose()}")
        # Sherman Morrison
        print(f"(a + uv^T)^(-1) is {ainv.sherman_morrison(u, v)}")