Question

If A and B are non-singular matrices of same order with det(A) = 5, then det(B⁻¹AB)² is equal to ______.

Options

• 5

• 5²

• 5⁴

• 5⁵

Answer 1

If A and B are non-singular matrices of same order with det(A) = 5, then det(B⁻¹AB)² is equal to 5². 

Explanation:

|A| = 5, |B⁻¹AB|² = (|B⁻¹||A||B|)² = |A|² = 5²