Special Matrices

Fun Class Activity:

1. What do we call a matrix that is both upper and lower triangular?
2. Which of the special matrices we covered are always sparse (no matter what elements we put in them?)
3. We covered 11 special matrix types. Consider the matrix: $$A = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{bmatrix}$$ Which of these types does $A$ belong to? There could be more than one special matrix whose format $A$ matches.