newtonian mechanics

Is momentum conserved when an object bounces back against a wall? The wall doesn’t move, but the object moves in the opposite direction. Assume this is an ideal, elastic collision.

I have a feeling this is wrong, so anybody clarify this for me?

Yes, it is wrong. You are wrong if you think that in an ideal, elastic collision the velocity of the bouncing object is exactly the same.

And also you are wrong if you think that the wall doesn't move. You can't see it move but it wouldn't only if it had infinite mass, which is impossible.

Suppose a mass of 1 kg hits a wall of 10, 000 kg at $v_0=10$ m/s. It has momentum 1*10 = 10 kg m/s. The formula for an elastic collision tells you that the wall will absorb momentum $ \frac {20}{10 001} = 2$ g m/s and the ball will keep $v'=9.9980002$ m/s.