If $ab=ba$, $\frac bx = \frac cz$ and $\frac ax = \frac dz$, does that mean that $ac=bd$?

Question

If $$ab=ba, \ \frac bx = \frac cz \quad\text{ and }\quad\frac ax = \frac dz$$ does that mean that $ac=bd $? I tried to prove this but couldn't.

Answer 1

If $\frac{a}{x}=\frac{d}{z}$, then $\frac{x}{a}=\frac{z}{d}$.

Now multiplying the equations together gives: $\frac{b}{x} \cdot \frac{x}{a}=\frac{c}{z} \cdot \frac{z}{d}$

$\frac{b}{a}=\frac{c}{d}$

See if you can proceed from here...