The matrix \( A=\begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix} \) is a
(A) Symmetric matrix
(B) Scalar matrix
(C) Diagonal matrix
(D) Skew-symmetric matrix
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (C) only
Every entry off the main diagonal of A is 0, and every diagonal entry is −3:
\( \displaystyle A=-3I \)
\( \displaystyle A^{T}=A \)
So A is diagonal with equal diagonal entries −3, \( A^{T}=A \), and its diagonal entries are not 0.
Checking the statements
(A) Symmetric matrix — Correct. \( A^{T}=A \), since every off-diagonal entry is 0.
(B) Scalar matrix — Correct. It is diagonal with all diagonal entries equal to −3.
(C) Diagonal matrix — Correct. All entries off the main diagonal are 0.
(D) Skew-symmetric matrix — Incorrect. A skew-symmetric matrix has every diagonal entry 0, but here the diagonal entries are −3.