[tex]\it \ d)\ \
\\ \\
I) \ detA= 3 \sqrt3 \cdot \sqrt3 - 2\sqrt2\cdot\sqrt2 =9-4=5[/tex]
[tex]\it II)\ A^t= \begin{pmatrix} \it \sqrt3&\it 2\sqrt2 \\ \\ \it \sqrt2&\it 3\sqrt3 \ \end{pmatrix} [/tex]
[tex]\it III)\ A^* =\begin{pmatrix} \it 3\sqrt3 &- \it \sqrt2
\\ \\
\it -2\sqrt2& \it \sqrt3 \end{pmatrix}[/tex]
[tex]\it IV)\ A^{-1} = \dfrac{1}{detA} \cdot A^* =\dfrac{1}{5}\cdot\begin{pmatrix} \it 3\sqrt3 &- \it \sqrt2 \\ \\ \it -2\sqrt2& \it \sqrt3 \end{pmatrix} =\begin{pmatrix} \it \dfrac{3\sqrt3}{5} &- \it \dfrac{\sqrt2 }{5} \\ \\ \it -\dfrac{2\sqrt2}{5} & \it \dfrac{\sqrt3}{5} \end{pmatrix} [/tex]
