Answer to Question #115677 in Linear Algebra for Sire

Question

A) Suppose A is a 3 x 3 matrix such that det (A) = 1/125 . Find det (5A^-1)


B)Suppose A is a 3 x 3 matrix such that det (A) = 5. Determine det [A^4]

Answer 1

A)$det(5A^{-1})=5^3det(A^{-1})=\frac{5^3}{det A}=5^6$ ;

B)$det(A^4)=(detA)^4=5^4.$