I have non-graphical calculator and I am strgguling to find way around to solve the imaginary matrix inverse becuase the calculator does not accept imaginary matrix.
I fould a way for solving if the matrix has just imaginary part such as $$ \begin{bmatrix} 1j & 3j \\ 2j & 4j \\ \end{bmatrix} $$
The inverse for this matrix can be found by find the inverse for $$ \begin{bmatrix} 1 & 3 \\ 2 & 4 \\ \end{bmatrix} $$
then multiply the matrix by $$ -j$$
The inverse equal
$$ \begin{bmatrix} -2 & \frac32 \\ 1 & - \frac12 \\ \end{bmatrix} *-j $$
The final form is
$$ \begin{bmatrix} 2j & -j\frac32 \\ -1j & j\frac12 \\ \end{bmatrix} $$
I am looking for a way to solve the following matrix by similar way:
$$ \begin{bmatrix} 3+1j & 2+3j \\ 3+2j & 2+4j \\ \end{bmatrix} $$
and
$$ \begin{bmatrix} 3+1j & 2+3j & 2+5j \\ 3+2j & 2+4j & 4+5j \\ 5+1j & 4+4j & 1+2j \\ \end{bmatrix} $$
The inverse of a $2\times 2$ matrix is given by $$ \begin{bmatrix}a&b\\c&d\end{bmatrix}^{-1}=\frac1{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}, $$ so you can calculate that explicitly. For a bigger matrix you could use row reduction, where again all you need to do are simple sums and multiplications.