Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=2, then det(A\)^3(I\) + \(A\)⁻^3)(I\) - \(A\)⁻^3)) equals:</p>
<p>(A) 1</p>
<p>(B) 2</p>
<p>(C) cannot be determined</p>
<p>(D) 4</p>
Step-by-Step Solution
Key Concept: Expression reduces to $A$^3(I$ - $A$⁻^6), still non-linear.
1. Expand \to $I$ - $A$⁻^6
2. Multiply with $A$^3
3. Contains subtraction \Rightarrow cannot determine
Correct Answer: 3