A. $\begin{bmatrix} 1 & 2 & 3\\2 & 4 & 5\\3 & 5 & 6\end{bmatrix}$ is a symmetric matrix
B. $\begin{bmatrix}0 & 0 & 0 \\0 & 0 & 0 \end{bmatrix}$ is a null matrix
C. $\begin{bmatrix} 1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix}$ is an Identity matrix
D. $\begin{bmatrix} 0 & 1 & 2\\-1 & 0 & 3\\-2 & 3 & 0\end{bmatrix}$ is a skew symmetric matrix
E. $\begin{bmatrix} \sqrt{3} & 0 & 0\\0 & \sqrt{3} & 0\\0 & 0 & \sqrt{3}\end{bmatrix}$ is a scalar matrix
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A, B, E only
(A) is correct. The matrix is symmetric because it is equal to its transpose $A = A^T$ with elements reflected perfectly across the main diagonal.
(B) is correct because all elements are zero, hence it is a null matrix.
(C) is false because in an identity matrix, all diagonal elements must be 1. Here the diagonal elements are 1, 2, and 3.
(D) is false because for a skew-symmetric matrix, the matrix must satisfy $ A^T$ = -A, which is not true here.
(E) is correct because all diagonal elements are equal and all non-diagonal elements are zero, so it is a scalar matrix.