Consider a $3\times 3$ matrix with every element being equal to 1 , its only non-zero eigenvalue is ....?
$3\times 3 \begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bmatrix}$
now i solve in simple way ..directly $\left | A-\lambda I \right |$ THEN I got correct ans 0,0,3 but
i have doubt .. if i solve by some elementary operation and reduce to $\begin{bmatrix} 1 & 1 &1 \\ 0& 0 &0 \\ 0 & 0 &0 \end{bmatrix}$
but i got different eigen values why this happened ... i missed something ??