The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is a

(A) Null matrix

(B) Unit matrix

(C) Symmetric matrix

(D) Skew-symmetric matrix

Choose the correct answer from the options given below:

The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ has all entries equal to 0.

A null matrix is a matrix where all elements are zero.

This matrix satisfies the condition for a null matrix.

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A unit matrix (identity matrix) must have 1's on the main diagonal and 0's everywhere else, such as $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$.

The given matrix has 0's on the diagonal, not 1's.

This is not a unit matrix.

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A matrix is symmetric if $A = A^T$ (the matrix equals its transpose).

Original: $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$

Transpose: $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$

Since $A = A^T$, this is a symmetric matrix.

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A matrix is skew-symmetric if $A^T = -A$ (transpose equals negative of the matrix).

$A^T = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$

$-A = -\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$

$-A = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$

Since $A^T = -A$, this is a skew-symmetric matrix.

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The matrix is a null matrix, symmetric matrix, and skew-symmetric matrix.

Therefore, the correct answer is (A), (C), and (D).