Step-by-Step Solution

1. Analyze the given matrix: The matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a diagonal matrix because all non-diagonal elements are zero.
2. Check if it's a scalar matrix: A scalar matrix is a diagonal matrix where all diagonal elements are equal. In this case, the diagonal elements are \(\sqrt{3}\), \(\sqrt{2}\), and \(\sqrt{5}\), which are not equal. Therefore, it is not a scalar matrix.
3. Check if it's an identity matrix: An identity matrix is a diagonal matrix where all diagonal elements are equal to 1. The given matrix does not have all diagonal elements equal to 1. Therefore, it is not an identity matrix.
4. Check if it's a null matrix: A null matrix has all elements equal to zero. The given matrix does not have all elements equal to zero. Therefore, it is not a null matrix.
5. Check if it's a symmetric matrix: A symmetric matrix is equal to its transpose. Since the given matrix is a diagonal matrix, it is equal to its transpose. However, the options do not include "diagonal matrix". The closest option would be a scalar matrix if the diagonal elements were equal. Since they are not equal, and "diagonal matrix" is not an option, we must consider the properties of the given matrix in relation to the provided options. The matrix is not symmetric in the general sense because a symmetric matrix A must satisfy A = A^T. While the given matrix equals its transpose, the options provided do not accurately describe the matrix. However, the question is flawed because none of the options are correct. The matrix is a diagonal matrix. The closest answer would be (A) if the diagonal elements were the same.