Question

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

Options

• Identity matrix

• Symmetric matrix

• Skew-symmetric matrix

• None of these

Answer 1

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

Explanation:

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

A' = ${\displaystyle \left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 4\end{array}\right]}$ = A

A' = A

So A is a symmetric matrix.