Question

Let $A=\left[a_{ij}\right]$ is a $3\times 3$ diagonal matrix and $k$ is the possible number of zeros in $A$. Then the sum of all possible value(s) of $k$ is

Answer 1

Given : $A=\left[a_{ij}\right],$ is a $3\times 3$ diagonal matrix.
So, maximum number of Zeros is $n^2-1=9-1=8$ and
minimum number of zeros is $n^2-n=9-3=6$ (where $n=3$ is order of matrix)
So, possible values of $k$ are $6,7,8$
$\therefore$ sum of values of $k=21$