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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
Let O be the given 3 × 3 zero matrix. Its transpose is O, and −O is also O.
Checking the statements
(A) Null matrix — Correct. Every entry is 0.
(B) Unit matrix — Incorrect. A unit matrix has every diagonal entry 1; here the diagonal entries are 0.
(C) Symmetric matrix — Correct. \(O^T = O\).
(D) Skew-symmetric matrix — Correct. \(O^T = O = -O\).
Tip: The zero matrix is the only matrix that is both symmetric and skew-symmetric: \(A^T = A\) and \(A^T = -A\) together give A = −A, so A = O.