Given are the following matrices:
$A_{1}=\begin{bmatrix} 4 & 7 &9 \\ 3 & 5 &3 \\ 1 &2 &0 \end{bmatrix}$ , $A_{2}=\begin{bmatrix} 10 & 9 &6 \\ 11 & 7 &2 \\ 5 &3 &0 \end{bmatrix}$ , $A_{3}=\begin{bmatrix} 14 & 11 &4 \\ 13 & 18 &6 \\ -18 &-4 &-2 \end{bmatrix}$ , $A_{4}=\begin{bmatrix} 11 & 13 &2 \\ 11 & 21 &3 \\ -13 &-5 &-1 \end{bmatrix}$
Which of them generate the same lattices? The lattices are generated by the rows of the basis matrices.
I calculated the determinants of the matrices and got $det\left | A_{1} \right |=det\left | A_{4} \right |=6$ and $det\left | A_{2} \right |=det\left | A_{3} \right |=18$. Is it a correct approach to solve the exercise? Do i have to do something more? Can anyone help me with this problem, please? Thank you in advance!