I was buildiing an amplifier circuit for +ve voltages only. When I used a 9V battery to supply V+ and V- (+ to V+, - to V-), I get a constant 8V at the output of the opamp. The output is not changing with respect to input. The circuit worked fine when I used a +/-12V dual power supply. However the way I understand it, using a single supply is okay as long as I'm not dealing with negative input voltages.
According to page 4 of the LM741 datasheet, the minimum supply voltage is +/- 10V, so powering it with +/-9V isn't guaranteed to work. The LM741 is a very old design, and its characteristics are not as good as modern op amps (that being said, it works fine, but it's not what I'd pick for a new design). I'd recommend getting a more modern op amp, you probably want one with rail to rail inputs and outputs as well as a lower minimum supply voltage. I've narrowed down the listing here, you still will want to make sure whatever you pick can use the supply you're planning to use.