Question

The rank of the matrix $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right],$ is

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is C 3

Given, $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$
Here, $|A|=5\ne 0$
Hence, rank of matrix$=$order of matrix $=3$