\(\begin{array}{l}
A = \left(\matrix{m&3\\-1&4}\right);\qquad B = \left(\matrix{-1&1\\-1&2}\right)\\
1)\\
\quad 2A + A.B^T - 5C = 0\\
\Leftrightarrow C = \dfrac25A + \dfrac15\cdot AB^T\\
\Leftrightarrow C = \dfrac25\left(\matrix{m&3\\-1&4}\right) + \dfrac15\left(\matrix{m&3\\-1&4}\right)\left(\matrix{-1&-1\\1&2}\right)\\
\Leftrightarrow C = \left(\matrix{\dfrac25m&\dfrac65\\-\dfrac25&\dfrac85}\right) + \left(\matrix{\dfrac15m&\dfrac35\\-\dfrac15&\dfrac45}\right)\left(\matrix{-1&-1\\1&2}\right)\\
\Leftrightarrow C = \left(\matrix{\dfrac25m&\dfrac65\\-\dfrac25&\dfrac85}\right) + \left(\matrix{\dfrac{-m+3}{5}&\dfrac{-m+6}{5}\\1&\dfrac95}\right)\\
\Leftrightarrow C = \left(\matrix{\dfrac{m+3}{5}&\dfrac{-m+12}{5}\\\dfrac35&\dfrac{17}{5}}\right)\\
2)\\
\quad BX.A\\
\Leftrightarrow B^{-1}.BX = B^{-1}.A\\
\Leftrightarrow X = \left(\matrix{-2&1\\-1&1}\right)\left(\matrix{m&3\\-1&4}\right)\\
\Leftrightarrow X = \left(\matrix{-2m -1&-2\\-m-1&1}\right)
\end{array}\)
