Solve the following equations
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: $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$

$A^{T}=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]^{T}$

$=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$

$=A$

Therefore, matrix $A$ is both diagonal and symmetric matrix.

Hence, the correct option is (b) and (d).