Find the inverse of 105 mod 4

Question

I did:

$$105 = 4*26+1\\ 1 = 105*1-4*26$$

So the inverse should be 5 as it is $\equiv 1 \pmod 4$ but it's 1. Why?

Answer 1

$1 = 105\cdot 1-4\cdot 26 = 105\cdot 1+(-4)\cdot 26$ tells us that the answer is $1$ (the multiplier of 105), which is the same as $5$, mod $4$.