Question

Which one of the following statements is not true?

• A. A scalar matrix is a square matrix.
• B. A diagonal matrix is a square matrix.
• C. A scalar matrix is a diagonal matrix.
• D. A diagonal matrix is a scalar matrix.

Answer 1

The correct option is D

A diagonal matrix is a scalar matrix.

A diagonal matrix is a matrix in which the all the elements outside the main diagonal are all zero.

A scalar matrix is a diagonal matrix where all the diagonal elements are equal.

Hence a diagonal matrix need not be a scalar matrix.
Example:
$\left[\begin{array}{cc}2& 0\\ 0& 4\end{array}\right]$