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Is there any function like Solve but designed to deal with matrix equations? Something like:

mA = {{1, 2}, {3, 4}};
mC = {{19, 22}, {43, 50}};
Solve[mA.mX == mC, mX]  (* should return {{5, 6}, {7, 8}} *)

I know that you could just type

Inverse[mA].mC

but I'm curious if there is other way to do this.

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    $\begingroup$ Get into the habit of using LinearSolve[] instead of Inverse[], whenever possible. $\endgroup$ – J. M.'s ennui♦ Jun 8 '16 at 18:18
  • $\begingroup$ @J.M. Thanks for advice. $\endgroup$ – Wilhelm Olejnik Jun 8 '16 at 18:35
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mA = {{1, 2}, {3, 4}};
mC = {{19, 22}, {43, 50}};
mX = Array[X, {2, 2}]
Solve[mA.mX == mC, Flatten[mX]]

Will do what you want

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