Diagonal Matrix Example
Diagonal matrices are square matrices in which all the elements outside the main diagonal are zero. A scalar matrix is a special case of a diagonal matrix where all the diagonal elements are equal. However, not all diagonal matrices are scalar matrices.

Example of a Diagonal Matrix
Consider the following matrix:
\[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} \]
In this matrix, all the elements outside the main diagonal are zero, making it a diagonal matrix. However, this matrix is not a scalar matrix because the diagonal elements are not all equal.

Explanation
In the given matrix A, the diagonal elements are 2, 3, and 4, which are different from each other. This means that the matrix is not a scalar matrix. Even though it is a diagonal matrix, it does not satisfy the condition of having all diagonal elements equal to be considered a scalar matrix.
Therefore, the matrix A serves as an example of a diagonal matrix that is not a scalar matrix. It showcases the distinction between diagonal matrices and scalar matrices, highlighting that not all diagonal matrices are scalar matrices.