An upper triangular matrix is a square matrix with all entries below the diagonal being zero. Suppose $A$ and $B$ are upper triangular matrices. Which of the following statements are true?
- The matrix $A+B$ is upper triangular.
- The matrix $A^T$ is upper triangular.
- The matrix $A^{-1}$ is upper triangular.
- The matrix $AB$ is upper triangular.
