What's wrong 1 pound=1 penny?

Question

Wheres the mistake?

1 pound = 100 penny

= 10 penny x 10 penny

= 1/10 pound x 1/10 pound

= 1/100 pound

= 1 penny

=> 1 pound = 1 penny

I feel its wrong in $3^{rd}$ step, but it isn't clear to me!!

Answer 1

Units.

10 pennies $\times$ 10 pennies is 100 (pennies$^2$), not 100 pennies; and similarly for pounds.

It's exactly the same as how there are 12 inches in a foot, but 144 square inches in a square foot.