Question

The matrix $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 4\end{array}\right]$ is

(a) identity matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) diagonal matrix

Answer 1

Given: $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 4\end{array}\right]$
​
$$\begin{gathered} A^T={\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 4\end{array}\right]}^T \\ =\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 4\end{array}\right] \\ =A \end{gathered}$$

Therefore, matrix A is both diagonal and symmetric matrix.

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