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? $$$2x+3y=5$$$ $$$3x+py=10$$$

The determinant of matrix $$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr 3 & 0 & 1 & 2 \cr } } \right]$$ is