Multiplicative inverses why two z in this formula?

Question

I am studying maths and have the following question set by my professor.

I thought the answer was 5, because: 3 . 5 = 15, and 15 mod 7 is 1. Since 1 mod 7 = 1 that means they match.

However, I looked at the formula and noticed both variables are z, which leads me to believe they both have to be 3. Look for the red in the picture. I guess my question is what the answer is, and why?

Answer 1

The first line, where you have underlined it in red, is the definition of $z^{-1}$. The next two lines are problems you are to do. Your answer of $5$ for the first is correct.

Answer 2

$3^{-1}\cong 5\pmod 7$ and $2^{-1}\cong3\pmod 5$. The first is because $3\cdot 5=15\cong1\pmod7$. The second because $2\cdot3=6\cong1\pmod5$.

Answer 3

The answer is that the z variables are different numbers, because one z is to the power of negative one.

The answer 5 was also correct for the example question.