Matrices & Determinants
Matrix equation — second determinant difference
MJAT_TS5_P2
Grade 12
Question:
**Paragraph (continued):** The value of $\det(A-4B)-\det(B-4A)$ is equal to:
Step-by-Step Solution
Key Concept: From the same matrix equation analysis, using the relation $\det(A-4B)-\det(B-4A)$. With $\det(B)=3$ and the constraints from $AB=A^2B^2-(AB)^2$.
$\det(A-4B)-\det(B-4A)=\mathbf{45}$.
Correct Answer: 45