I implemented a basic circuit as attached here in photo along with its
output. Is the output as it should be?
That output looks like ordinary A + B (rather than A × B) and, if I examine your circuit, indeed that is what it is (a summing amplifier). Of course there may be a tiny amount of "A × B" lurking in the overall signal but, for producing amplitude modulation, it is highly (if not totally) inefficient.
what am I doing wrong, and how can I make the necessary changes?
I'll suggest a diode multiplier (the simplest form of "double sideband plus carrier" amplitude modulation) as a solution: -

This is a 1 MHz carrier AM modulator and can be received on a standard AM radio receiver in the MW band: -


Images can be found here or here.