# Determinant properties. Am I right?

If A,B 3 x 3 matrix. If $\det(A) = 3, \det(B) = 2$. Find the determinant of the following:

$(2A^{-1}), 3(B)^{-1}, (5A)B^{-1}$

Respectively

$\frac{2^3}{3}, \frac{3^3}{2}, \frac{5^3}{2}$

Is that right?

• Are you sure about those parens in the second expression? Do you mean $3(B^{-1})$ or $(3B)^{-1}$? If it's the first, you're correct. As @Peter correctly points out the third answer is missing a factor of $3$. Mar 30 '17 at 20:08
• Yes, I deleted this comment however because Ollie mentions it in the answer Mar 30 '17 at 20:12

The first two are correct but $\det(5AB^{-1}) = \frac{3 \cdot 5^3}{2}$.