M=$\begin{pmatrix} -a+\lambda &2 &3 \\ 1&-2b+2\lambda &3 \\ 1&2 & -3c+3\lambda \end{pmatrix}$=0
can be written as:-
M=$\begin{pmatrix} -a &2 &3 \\ 1&-2b &3 \\ 1&2 & -3c \end{pmatrix}$ / -6 - $\lambda$/-6 $\begin{pmatrix} -1 &0 &0 \\ 0&-2 &0 \\ 0&0 & -3 \end{pmatrix}$=0
|M'-$\lambda$I|=0
:represent $\lambda$ is eigen values of given matrix.....and product of all the values of is equal to the determinent of matrix M' /-6
M'=$\begin{pmatrix} -a &2 &3 \\ 1&-2b &3 \\ 1&2 & -3c \end{pmatrix}$ /-6
Det(M')devided by -6=option C