Question

The rank of the matrix,$A=\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]$is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is D 3

$A={\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]}_{3\times 3}$
$|A|=0(0-1)-1(0-1)+1(1-0)=2$
The rank of matrix A will be 3 because $|A{|}_{3\times 3}\ne 0$