Lighting, Light Fixtures, Ceiling and Exhaust Fans - New switch in garage

My garage has the light switch at the front of the garage, and I want to add one at the back door of the garage. Presently the power comes from the house to a receptacle in the garage, then to the light, then to a single pole switch at the front of the garage. It is all two wire cable, black, white and ground.
I have detached the light from the receptacle and run it to a new switch box at the back door of the garage and then run a separate cable from the same switch box to the receptacle. Can I use a single pole switch on the new switchbox or do I need a three way switch, and if so do I also need three wire cable?

If you want to be able to control the light from either location independently then the simplest thing is to add a three wire+grd cable from the existing switch to the new switch location.

OK, I did as instructed, and the light works if I switch it on/off from the back door or if I switch on/off from the front door. However, if I switch the light on from the back door and then switch it off from the front door, then try to switch it on again from the back door, it doesn't work. What did I do wrong? :(

You incorrectly identified which wire is the "common" on one or both switches. Or you didn't use a pair of 3-way switches.

Describe your connections in more detail, including identifying the color and cable of each wire, and the color of each screw.

OK, here is how I wired it. Both front and rear light switches are 3-way, and the cable between them is 14/3. I attached the red wire to common (black screw), the black wire to the gold screw on the same side of the switch, the white wire to the gold screw on the opposite side, same for both switches. At the light I wired the two reds to each other and the two whites to each other from the switches, the black from the front switch is wired to the black from power, and the white from power cable is wired to the light, the black from the rear switch is wired to the light. (The light is just a common socket type with four screws, two on each side of the base, I wired the white to the screw on one side and the black to the screw on the other side).

At both switches, swap the black and red wires (i.e., put the black wire on the black screw).

That fixed it! Thanks so much for your help. :)