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?

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 :

For what value of $$'p'$$ the following set of equations will have no solutions? $$$2x+3y=5$$$ $$$3x+py=10$$$