(A) Scalar matrix
(B) Diagonal matrix
(C) Skew-symmetric matrix
(D) Symmetric matrix

Choose the correct answer from the options given below:

The correct answer is: (A), (B), and (D) only.

Based on the provided image, the matrix to classify is the identity matrix of order 3, denoted as:
$$I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$

We analyze each of the given classifications step-by-step:

1. Diagonal matrix (B):
A square matrix is classified as a diagonal matrix if all its non-diagonal elements are zero. Formally, for a matrix $A=\left[a_{ij}\right]$, it is a diagonal matrix if $a_{ij}=0$ for all $i\ne j$.
For the given matrix, all off-diagonal elements are indeed $0$. Therefore, it is a diagonal matrix. Statement (B) is correct.

2. Scalar matrix (A):
A diagonal matrix is classified as a scalar matrix if all of its main diagonal elements are equal to a single scalar value. Formally, $a_{ii}=k$ for all $i$, where $k$ is a constant.
For the given matrix, the diagonal elements are:
$$a_{11}=a_{22}=a_{33}=1$$
Since all main diagonal elements are equal to $1$, it is a scalar matrix. Statement (A) is correct.

3. Symmetric matrix (D):
A square matrix $A$ is symmetric if it is equal to its transpose, meaning $A^T=A$. Taking the transpose of $I$ by swapping its rows and columns gives:
$$I^T=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]=I$$
Since $I^T=I$, the matrix is a symmetric matrix. Statement (D) is correct.

4. Skew-symmetric matrix (C):
A square matrix $A$ is skew-symmetric if $A^T=-A$. This definition requires the main diagonal elements to satisfy $a_{ii}=-a_{ii}$, which is only possible if all diagonal elements are $0$.
Since the main diagonal elements of the given matrix are all $1$, and:
$$-I=\left[\begin{array}{ccc}-1& 0& 0\\ 0& -1& 0\\ 0& 0& -1\end{array}\right]\ne I^T$$
The matrix is not a skew-symmetric matrix. Statement (C) is incorrect.

Comparing our findings, statements (A), (B), and (D) are correct, which corresponds to the option (A), (B), and (D) only.