Answer:
-864
Step-by-step explanation:
The determinant of a matrix product is the product of the determinants. The determinant of a transpose is the same as the determinant of the original. Hence ...
[tex]|AB^5C^T|=(4)(-2)^5(\frac{1}{4})=-32[/tex]
The multiplication of an n×n matrix by a scalar 'a' multiplies its determinant by a^n, so the desired determinant is ...
[tex]|3AB^5C^T|=3^3(-32) = \boxed{-864}[/tex]
