The matrix $\left[ {\begin{array}{llllllllllllllllllll}1&0&0\\0&2&0\\0&0&4\end{array}} \right]$ is a

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

$\therefore$ ${A^\prime } = \left[ {\begin{array}{llllllllllllllllllll}1&0&0\\0&2&0\\0&0&4\end{array}} \right] = A$

Therefore, the given matrix is a symmetric matrix.

[since, in a square matrix A, if ${A^\prime } = A$, then A is called symmetric matrix]