The square wave inveter is the simplest kind of inverter:
Just take four power (or six for three phase application) transistors, arrange them as a full bridge and drive them with signals of the desired output frequency (and approbiate polarity)
Basically it is a DPDT (double pole double throw) switch.
It connects one side of the load to the positive, the other side to the negative pole of the DC power supply for T time and following this switches to the opposite polarity for the same time.
Time diagram of the two sides of the load:
1.) __--__--__--
2.) --__--__--__
where "_" = -Vsupply and "-" = +Vsupply.
The only complication: The switch must not short the
supply + to -.
Suggestion: Any active dc amplifier inverter can invert the square wave, unless you mean the dc-ac inverter having the output resembling the square wave. Then, any chopper, clamper, etc. will approximately do.