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Let L, M, and N be non-singular matrices of order 3 satisfying the equations L² = L⁻¹, M = L⁸ and N = L². Which ONE of the following is the value of the determinant of (M - N)?
- 0
- 1
- 2
- 3
Correct answer: 0
Solution
Since L² = L⁻¹, we can deduce that L⁸ = (L²)⁴ = (L⁻¹)⁴ = (L⁴)⁻¹. Therefore, M = L⁸ = (L⁴)⁻¹ and N = L². This implies that M and N are inverses of each other, leading to M - N being singular, which results in a determinant of 0.
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