The question says,
"Let $X=\{x_1,x_2,…,x_n\}$ and $X’=\{x’_1,x’_2,…,x’_n\}$ be two bases of $F^n$. Let $A=[x_1 :…:x_n]$ and $B=[x’_1:…:x']$. Show that the matrix of transition from $X$ to $X’$ is $A^{-1}B$. "
My attempt: If $R$ be the matrix of transition from $X$ to $X’$ and if $a$ and $b$ be the representation of a certain vector of $F^n$ with respect to the coordinate system of $X$ and $X’$ respectively then $Rb=a$. So, $Rx’_1= x_1$,$Rx'_2=x_2$,….$Rx’_n=x_n$. Which implies $RB=A$ ,i.e. $R=AB^{-1}$.
What am I missing here? Any help would be appreciated.