Two matrices A and B are given below:
\[{\text{A}} = \left[ {\begin{array}{*{20}{c}} {\text{p}}&{\text{q}} \\ {\text{r}}&{\text{s}} \end{array}} \right]{\text{;}}\,{\text{B}} = \left[ {\begin{array}{*{20}{c}} {{{\text{p}}^2} + {{\text{q}}^2}}&{{\text{pr}} + {\text{qs}}} \\ {{\text{pr}} + {\text{qs}}}&{{{\text{r}}^2} + {{\text{s}}^2}} \end{array}} \right]\]
If the rank of matrix A is N, then the rank of matrix B is

A. \[\frac{{\text{N}}}{2}\]

B. N - 1

C. N

D. 2N

Answer: Option C