Find the Products AB and BA to Determine Whether B $\mathrm { A } = \left[ \begin{array} { r r } 4 & - 3 \\ - 4 & 0 \end{array} \right]$

question 151

Multiple Choice

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
- $\mathrm { A } = \left[ \begin{array} { r r } 4 & - 3 \\ - 4 & 0 \end{array} \right]$

• A)
• \(\left[ \begin{array} { r } 0 - \frac { 1 } { 4 } \\ - \frac { 1 } { 3 } - \frac { 1 } { 3 } \end{array} \right]\)
• B)
• \(\left[ \begin{array} { c r } 0 & \frac { 1 } { 4 } \\ \frac { 1 } { 3 } & - \frac { 1 } { 3 } \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } - \frac { 1 } { 3 } - \frac { 1 } { 3 } \\ 0 - \frac { 1 } { 4 } \end{array} \right]\)
• D)
• \(\left[\begin{array}{c}
• -\frac{1}{3}-\frac{1}{4} \\
• -\frac{1}{3} 0
• \end{array}\right]\)

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Definitions:

Ethical Egoism

A moral philosophy arguing that individuals should act in their own self-interest and that this is the only moral duty.

Altruistic Explanations

Theories or reasons provided for actions taken for the benefit of others, often without personal gain and sometimes at a cost to oneself.

Stoicism

A classical Greek philosophical approach that emphasizes cultivating self-discipline and resilience to conquer harmful feelings.

Virtue Ethics

An ethical theory that emphasizes the role of character and virtue in moral philosophy rather than either doing one’s duty or acting to bring about good consequences.