P/E calculated from P/B and ROE?

CFA Level I FRA
#1

I just saw this article where it says you can calculate P/E using this formula. P/E = P/B / ROE
I have never seen this relationship before. Is this a correct formula?

#2

\frac{P}{B} = \frac{P}{E} \times \frac{E}{B}

\frac{P}{B} = \frac{P}{E} \times ROE

\frac{P}{E} = \frac {\frac{P}{B}}{ROE}