You can think of A and B as being the equivalent of left and right (and it doesn't matter which way round you use them). Professional equipment is often labelled in this way as an amp like yours might be used to drive one bass channel and one treble channel, depending on the setup, so left and right doesn't apply here.
Of the two sockets for channel A, you can plug your mixer into either, and the other is then available to take the same signal you're feeding into it off elsewhere (you could feed a second, different amplifier for a subwoofer, for example).
So, in summary, yes, plug one channel output of your mixer into one of the 'A' sockets and the other channel into one of the 'B' sockets. Plug your speakers into the A and B outputs (remembering to match the left and right to the inputs of course) and let rip!
Engineers: fixing problems you didn't know you had in ways you don't understand.