To find the multiplicative inverse of each nonzero element in Z₅, then need to find a value for each element that, when multiplied by the original element, gives a remainder of 1 when divided by 5.

In Z_5, the nonzero elements are {1, 2, 3, 4}.

Let's calculate the multiplicative inverse for each element:

1: 1 * 1 ≡ 1 (mod 5) The multiplicative inverse of 1 is 1 itself.

2: 2 * 3 ≡ 1 (mod 5) The multiplicative inverse of 2 is 3.

3: 3 * 2 ≡ 1 (mod 5) The multiplicative inverse of 3 is 2.

4: 4 * 4 ≡ 1 (mod 5) The multiplicative inverse of 4 is 4 itself.

Therefore, the multiplicative inverses of the nonzero elements in Z₅ are:

1 → 1

2 → 3

3 → 2

4 → 4