Question Number 204211 by mnjuly1970 last updated on 08/Feb/24
Answered by witcher3 last updated on 08/Feb/24
$$\mathrm{detA}=\mathrm{7}=\overset{−} {\mathrm{0}}\:\:\mathrm{in}\:\mathbb{Z}/\mathrm{7}\mathbb{Z} \\ $$$$\mathrm{A}\notin\mathrm{GL}\left(\mathrm{2};\mathbb{Z}/\mathrm{7}\mathbb{Z}\right) \\ $$$$ \\ $$
Commented by mnjuly1970 last updated on 08/Feb/24
$$\:\:{you}\:{are}\:{right}\:.\:{i}\:{corrected}\:{it}. \\ $$
Answered by AST last updated on 08/Feb/24
$${A}=\begin{pmatrix}{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{4}}&{\mathrm{5}}\end{pmatrix}=\begin{pmatrix}{\mathrm{3}}&{\mathrm{2}}\\{−\mathrm{3}}&{−\mathrm{2}}\end{pmatrix}\Rightarrow\mid{A}\mid=−\mathrm{6}−\left(−\mathrm{6}\right)=\mathrm{0} \\ $$