Let $y$ be a non-zero vector of size $2022 \times 1.$ Which of the following statement(s) is/are $\text{TRUE}?$

1. $yy^{T}$ is a symmetric matrix.
2. $y^{T}y$ is an eigenvalue of $yy^{T}.$
3. $yy^{T}$ has a rank of $2022.$
4. $yy^{T}$ is invertible.