If A is a 6 by 6 matrix and det A 9 then det 3 middot A

If A is a 6 by 6 matrix and det (A) = ? 9 then: det (? 3 middot A) = __________________ det (A^?1) =________________ det ( ? A) =_________________ det ((? 3 middot A)^?1) =______________ det (? 3 middot A)^?1) =______________

Solution

Ue properties of determinants

a) det(-3A) =( -3)^6*detA = 729*(-9) = -6561

b) det(A^-1) = 1/detA = -1/9

c) det(-A) = (-1)^6detA = -9

e) det(-3*A^-1) = (-3)^6/detA = 3^6/-9 = -81