Example of a Diagonal Matrix Which is Not Scalar

Concept Used

A diagonal matrix has all non-diagonal elements equal to zero.

A scalar matrix is a diagonal matrix in which all diagonal elements are equal.

So, for a diagonal matrix to be not scalar, its diagonal elements must be different.

Example

\[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix} \]

Explanation

– All non-diagonal elements are zero → so it is a diagonal matrix

– Diagonal elements (1, 2, 3) are different → so it is not a scalar matrix

Final Answer

\[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix} \]