Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^4(A\)⁻^4 + \(I)(A\)⁻^4 - \(I)) equals:</p>
<p>(A) 1</p>
<p>(B) -1</p>
<p>(C) cannot be determined</p>
<p>(D) 9</p>
Step-by-Step Solution
Key Concept: Product reduces to subtraction \to determinant cannot be computed.
1. Expand \to $A$⁻^8 - $I$
2. Multiply by $A$^4
3. Contains subtraction \Rightarrow cannot determine
Correct Answer: 3