MHB Solving for X in Matrix Equation: C^TA-XB=B^{-1}-X

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I have to express $X$ in given matrix equation:

$$C^TA-XB=B^{-1}-X$$

I have done this,and i don't know if i have done it good:
$$C^TA-B^{-1}=XB-X$$
$$C^TA-B^{-1}=X(B-I)$$

$$(C^TA-B^{-1})(B-I)^{-1}=X$$

Thank you for the help and answers!
 
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Yes, that is correct (assuming, as you have to, that $B-I$ is invertible).
 
Opalg said:
Yes, that is correct (assuming, as you have to, that $B-I$ is invertible).

Thank you! I really hope it is correct! ;)

I haven't noticed similar examples on the internet,do you maybe know where i could find them?
 
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