Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=2, then det(A\)^3(A\)⁻^3 + \(I)(A\)⁻^3 - \(I)) equals:</p>
<p>(A) 1</p>
<p>(B) -1</p>
<p>(C) cannot be determined</p>
<p>(D) 4</p>
Step-by-Step Solution
Key Concept: Expansion leads to difference of matrices, still not solvable.
1. Expand product \to $A$⁻^6 - $I$
2. Expression = $A$^3(A$⁻^6 - $I)
3. Cannot simplify determinant
Correct Answer: 3