Find the Products AB and BA to Determine Whether B

question 67

Multiple Choice

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
- $A = \left[ \begin{array} { l l } - 5 & 1 \\ - 7 & 1 \end{array} \right] , \quad B = \left[ \begin{array} { l } \frac { 1 } { 2 } - \frac { 1 } { 2 } \\ \frac { 7 } { 2 } - \frac { 5 } { 2 } \end{array} \right]$

• A) \(B = A ^ { - 1 }\)
• B) \(B \neq A ^ { - 1 }\)

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Definitions:

Illumination

Refers to the quality or state of being lit or the process of illuminating a specific area, often used metaphorically to mean clarifying or enlightening an issue or topic.

Keenness of Insight

The ability to see or understand things clearly and deeply, often leading to intuitive judgments.

Fortunate Accident

An unexpected event that leads to a positive outcome or benefit, often playing a valuable role in discoveries and innovations.

Creativity

The ability to generate novel and valuable ideas, solutions, or works that are original and imaginative.