Question:
The matrix $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$ is
(a) identity matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) diagonal matrix
Solution:
Given: $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$
$A^{T}=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]^{T}$
$=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$
Therefore, matrix $A$ is both diagonal and symmetric matrix.
Hence, the correct option is (b) and (d).
$=A$