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.
- $$A = \left[ \begin{array} { r r r r } 2 & 0 & 1 & 1 \\1 & 1 & - 1 & - 1 \\- 1 & - 2 & 1 & 0 \\0 & 0 & 1 & 1\end{array} \right] , \quad B = \left[ \begin{array} { r r r r } 2 & 0 & 0 & - 2 \\- 2 & 1 & 0 & 3 \\- 2 & 2 & 1 & 5 \\2 & - 2 & - 1 & - 3\end{array} \right]$$

A) $B \neq A ^ { - 1 }$
B) $\mathrm { B } = \mathrm { A } ^ { - 1 }$ Find the inverse of the matrix, if possible.