The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is

Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and $${{a_{ij}} = i.j.}$$
The rank of $$A$$ is :