關於可逆的整體等價式?請問有誤嘛!? 謝^^

A:mxn.則下列敘述等價
A nosigular
<=>A行獨立 in F^(nx1)
<=>A行生成 in F^(nx1) ie.(CS(A)=F^(nx1))
<=>A行基底 for F^(nx1)
<=>A列生成 in F^(1xn)
<=>A具左反
<=>AX=0只有0解 ie.(ker(A)={0}<=>ker(A^(H) x A)={0})<=>A^(H) x A 可逆
<=>rank(A)=n & (rank(A^(H) x A)=n)
<=>A列等價於I