Isolation transformer again

[Bondguy]

I bought an isolation transformer and prepared it for my need.
Now it has Live, Neutral and Ground pins connected to  primary side of the transformer.
Live and Neutral pins to secondary side.( No Ground on secondary)
Is that  correct ?

Now I want to measure ,with  a oscilloscope ,on live side of a power supply( SMPS) adaptor.
So, I connect that tested power supply adaptor to a secondary side of the isolation transformer.
But must I also connect the scope to the secondary side of the isolation transformer or I not?
May I connect the scope to a common wall  outlet?

[DmitryL]

Are you sure that you want to mess with mains stuff if you have no idea how it works and how to connect wires properly without killing yourself ?

[Bondguy]

That is a reason why I asked to understand properly

[DmitryL]

There was a video here "how not to blow your oscilloscope"

[madires]

But it might be a better idea to get some nice differential probes, from Pintek for example.