Solution:     

Matrix A is a scalar matrix (because its diagonal entries are same).

Matrix B is a diagonal matrix (because its diagonal entries are non-zero and non-diagonal entities are zero).

Matrix C is an identity matrix (because its diagonal entries are $1$).

Matrix D is a diagonal matrix (because its one diagonal entry is non-zero and non-diagonal entities are zero).

Matrix E is a scalar matrix (because its diagonal entries are same).

E = $\left[ \begin{matrix}    5-3 & 0  \\    0 & 1+1  \\ \end{matrix} \right]$            

E = $\left[ \begin{matrix}    2 & 0  \\    0 & 2  \\ \end{matrix} \right]$

Note:

All the matrices A, B, C, D and E are diagonal matrices because they have at least one non-zero diagonal entry and all their non-diagonal entries are zero. Scalar and unit matrices are further types of diagonal matrices.