Matrices And Determinants

$M$ is invertible

There exists a nonzero column matrix $\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right)$ such that $M\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right)=\left(\begin{array}{l}-a_1 \\ -a_2 \\ -a_3\end{array}\right)$

The set $\left\{X \in \mathbb{R}^3: M X=\mathbf{0}\right\} \neq\{\mathbf{0}\}$, where $\mathbf{0}=\left(\begin{array}{l}0 \\ 0 \\ 0\end{array}\right)$

The matrix $(M-2 I)$ is invertible, where $I$ is the $3 \times 3$ identity matrix