Find the Products AB and BA to Determine Whether B

Multiple Choice

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
- $$A = \left[ \begin{array} { r r r r } 1 & 0 & 0 & - 1 \\2 & 1 & 0 & 0 \\1 & 1 & 1 & - 2 \\0 & 0 & 0 & 1\end{array} \right] , \quad B = \left[ \begin{array} { r r r r } 1 & 0 & 0 & 1 \\- 2 & 1 & 0 & - 2 \\1 & - 1 & 1 & 3 \\0 & 0 & 0 & 1\end{array} \right]$$

A) $B = A ^ { - 1 }$
B) $B \neq A ^ { - 1 }$