Going from $X^tAB - I = X^t$ to $X^t(AB-I) = I$ in matrix algebra. Finding the value of the matrix $X$:
$$X^tAB - I = X^t$$
I noticed that the next step chosen by my book is
$$X^t(AB-I) = I$$
It's not clear to me how did they reach that. How did they go from one step to the other, exactly?

This is just:$$X^tAB - I = X^t
\iff
X^tAB - X^t = I
\iff
X^t(AB - I) = I
$$
