Tension and Gravity- Quick answer

This is mostly just to clarify & make sure I have my information correct.

If you have an elevator at rest or moving up or down at constant velocity, the tension force is equal magnitude and opposite direction to the force of gravity (mg), according to Newton's First Law.

If an elevator is accelerating upward, the tension force is greater than the force of gravity. If it is accelerating down, the force of gravity is greater than the tension force.

Are all of these statements correct? If not, could you please explain where I am wrong?

This is mostly just to clarify & make sure I have my information correct.

If you have an elevator at rest or moving up or down at constant velocity, the tension force is equal magnitude and opposite direction to the force of gravity (mg), according to Newton's First Law.

If an elevator is accelerating upward, the tension force is greater than the force of gravity. If it is accelerating down, the force of gravity is greater than the tension force.

Are all of these statements correct? If not, could you please explain where I am wrong?