$$A$$ is $$m$$ $$x$$ $$n$$ full rank matrix with $$m > n$$ and $${\rm I}$$ is an identity matrix. Let matrix $${A^ + } = {\left( {{A^T}A} \right)^{ - 1}}{A^T}.$$ Then which one of the following statement is false?

If the rank of a $$5x6$$ matrix $$Q$$ is $$4$$ then which one of the following statements is correct?

The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as
$$\alpha \left( \lambda \right) = \left| {\lambda {\rm I} - P} \right| = {\lambda ^3} + 2\lambda + {\lambda ^2} + 1 = 0.$$
If $${\rm I}$$ denotes identity matrix then the inverse of $$P$$ will be

In the single phase voltage controller circuit shown in the figure, for what range of triggering angle $$\left( \alpha \right)$$, the output voltage $$\left( {{V_0}} \right)$$ is not controllable?