2. "2 times row one of $A^{-1}$ minus row two of $A^{-1}$ plus 3 times row 3 of $A^{-1}$" is simply $\begin{bmatrix}2 & -1 & 3\end{bmatrix}A^{-1}$. But that is the second row of A. Multiplying the second row of A by $A^{-1}$ gives the second row of the identity matrix which is $\begin{bmatrix}0 & 1 & 0\end{bmatrix}$.