Find the Products AB and BA to Determine Whether B

question 21

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.

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Definitions:

Elimination By Aspect

A decision-making process where alternatives are systematically rejected based on the absence or presence of certain attributes.

Satisficing

A decision-making strategy which aims for an adequate rather than the optimal solution, prioritizing sufficiency over perfection.

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