Two matrices $A$ and $B$ are given below:

$A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$ ;     $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$

If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is

1. $N/2$
2. $N$-$1$
3. $N$
4. $2N$

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