Question

If $a_{ij}=0(i\ne j)$ and $a_{ij}=2(i=j)$ then the matrix A=${\left[a_{ij}\right]}_{n\times n}$ is a _______ matrix

• A. unit
• B. null
• C. scalar
• D. skew symmetric

Answer 1

Answer: (C)

scalar

Given $A$ is a square matrix as the number of rows and columns are same as $n$.
We know that the elements $a_{ij}$ where $i=j$ lie along the diagonal and the elements $a_{ij}$ where $i\ne j$ do not lie along the diagonal.
Given, diagonal elements $=2$ and the rest of the elements $=0$
Such a diagonal matrix where all diagonal elements are equal, is called a scalar matrix.