The system $\mathrm{AX}=\mathbf{0}$ is _____.

In a non-homogeneous system $\mathrm{AX}=\mathrm{B}$ , if $\rho \left(A\right) = \rho \left(A\right|B) <$ number of unknowns, then the system is _____.

The system of linear equations $\mathrm{x}+\mathrm{y}+\mathrm{z}=3, \mathrm{x}+2\mathrm{y}+3\mathrm{z}=4 \& \mathrm{x}+4\mathrm{y}+\mathrm{kz}=6$ will not have a unique solution for $\mathrm{k}$ equal to ______.

Let $\mathrm{A}=\left[\begin{array}{cc}1& 4\\ 2& 3\end{array}\right]$ . Then $\mathrm{A}$ satisfies the equation _____.

If a characteristic equation of a $3\times 3$ matrix $\mathrm{A}$ is ${\mathrm{\lambda }}^3-6{\mathrm{\lambda }}^2+9\mathrm{\lambda }-4=0$ , then ${\mathrm{A}}^{-1}=$ _____.

If $\mathrm{AX}=\mathrm{B}$ is a system of n linear equations in n variables such that $\left|\mathrm{A}\right|\ne 0$ , then the system has _____.

If $\mathrm{A}=\left(\begin{array}{ccc}-1& 0& 3\\ 0& 2& 0\\ 0& 0& 1\end{array}\right)$ , then the eigen values of ${\mathrm{A}}^3$ are _____. 

If $\mathrm{B}=\left(\begin{array}{ccc}1& 0& 0\\ 2& 3& 4\\ 0& -2& 5\end{array}\right)$ . Then the product of the eigen values of $\mathrm{B}$ is _____.

Let $\mathrm{A}=\left(\begin{array}{cc}2& 7\\ -1& -3\end{array}\right)$ . Then ${\mathrm{A}}^{-1}=$ _____.

A square matrix $\mathrm{B}$ is diagonallizable, if it is similar to _____.