A reason why Internet is not recommended for beginners

I could not get, withinh the time I spent a nice short description or a video explaining the scalar and vector potentials from scratch.

Here I reproduce two examples I stumbled upon, while searching for suitable page/video for a quick reminder of scalr and vector potentials. These videos on You Tube show hazards of learning from internet. I have reproduced only the relevant parts of the videos.

FIRST VIDEO : Watch from time 1:30 to 3:05 sec
The speaker cancels div in equation
\[\text {div} B = \text{div . curl }A\]
and gets \(B=\text{curl} A\)

Click to Play First Video

SECOND VIDEO: Watch from time 0:50 to 2:00 Mins
The speaker compares \[ div B = 0 \qquad \text{and} \qquad  div curl A=0 ]\  and concludes the equality
\(B=curl A\)

 Click toPlay Second Video

 If you accept the logic given in these two videos, you can prove anything equals anything.
So, for example, it is definitely correct that \(\text{div 5} =\text{div} 37\), because both sides are zero.
It should then follow that \(5=37\),
I wish life was a simple as made out in the two videos.
The correctness of the final answer does not justify the means of getting the result.