Answer
B is the inverse of A
Work Step by Step
When there is an inverse of a matrix $A A^{-1}$ = I (the Identity Matrix)
AB = $\begin{bmatrix}
1(2) + 1(-1) & 1(1) + -1(1) \\
2(-1) +2(1) & (-1)(1) + 1(2)\\
\end{bmatrix}$ = $\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$
Since AB equals the identity matrix, B is the inverse of A.
