Problem 58787. Solve the matrix equation AXB + X + C = 0 for X

Let A, B, and C be square matrices of equal size, and let the matrix X be defined by the matrix equation
A * X * B + X + C = 0
Please solve this equation for X. For instance, if
A = [1 2 ; 3 4];
B = [5 6 ; 7 8];
C = [9 10 ; 11 12];
then
X = [-1/2 5/3 ; -19/6 1];
solves the equation, as is easily checked. You may assume that A, B and C are such that a solution exists.
Solve

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71.43% Correct | 28.57% Incorrect
Last Solution submitted on Jul 31, 2024

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