设 $\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{s}$ 均为 $n$ 维列向量, $\boldsymbol{A}$ 是 $m \times n$ 矩阵,下列选项正确的是( )
A. 若 ${\alpha}_{1}, {\alpha}_{2}, \cdots, {\alpha}_{s}$ 线性相关, 则 ${A} {\alpha}_{1}, {A} {\alpha}_{2}, \cdots, {A} {\alpha}_{s}$ 线性相关.
B. 若 ${\alpha}_{1}, {\alpha}_{2}, \cdots, {\alpha}_{s}$ 线性相关, 则 ${A} {\alpha}_{1}, {A} {\alpha}_{2}, \cdots, {A} {\alpha}_{s}$ 线性无关.
C. 若 ${\alpha}_{1}, {\alpha}_{2}, \cdots, {\alpha}_{s}$ 线性无关, 则 ${A} {\alpha}_{1}, {A} {\alpha}_{2}, \cdots, {A} {\alpha}_{s}$ 线性相关.
D. 若 ${\alpha}_{1}, {\alpha}_{2}, \cdots, {\alpha}_{s}$ 线性无关, 则 ${A} {\alpha}_{1}, {A} {\alpha}_{2}, \cdots, {A} {\alpha}_{s}$ 线性无关.