Find the Inverse of a If It Has One, or State

question 97

Multiple Choice

Find the inverse of A if it has one, or state that the inverse does not exist.
- $$A = \left[ \begin{array} { r r } 2 & 8 \\3 & 12\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r }
• 12 & - 8 \\
• - 5 & 3
• \end{array} \right]\]
• B) Inverse does not exist
• C)
• \[\left[ \begin{array} { r r }
• 12 & - 8 \\
• - 3 & 2
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { c c }
• \frac { 1 } { 2 } & 0 \\
• 0 & \frac { 1 } { 12 }
• \end{array} \right]\]

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Definitions:

Complement

A good or service that is used together with another good or service, increasing its demand.

Income Increase

A rise in the amount of money received by individuals or entities, typically through earnings, investments, or bonuses.

Normal Good

A good for which demand increases when consumer income rises, and falls when consumer income decreases, all other factors being equal.

Student Income

The amount of money earned or received by students from employment, grants, stipends, or other sources while pursuing their studies.