设 $\boldsymbol{A}=\left(\begin{array}{cccc}a_{1} b_{1} & a_{1} b_{2} & \cdots & a_{1} b_{n} \\ a_{2} b_{1} & a_{2} b_{2} & \cdots & a_{2} b_{n} \\ \vdots & \vdots & & \vdots \\ a_{n} b_{1} & a_{n} b_{2} & \cdots & a_{n} b_{n}\end{array}\right)$, 其中 $a_{i} \neq 0, b_{i} \neq 0(i=1,2, \cdots, n)$, 则矩阵 $\boldsymbol{A}$ 的秩 $r(\boldsymbol{A})=$