1. **Problem:** Identify the matrix given: \[ \left[\begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right] \] 2. **Explanation:** This is an upper triangular matrix where all elements below the main diagonal are zero. 3. **Key properties:** - The diagonal elements are all 1. - Such a matrix is invertible because all diagonal entries are non-zero. 4. **Intermediate work:** No further simplification needed; the matrix is already in upper triangular form. 5. **Conclusion:** The matrix is an upper triangular matrix with ones on the diagonal. Final answer: The matrix is an upper triangular matrix with diagonal entries all equal to 1.