Question

Let A and B be 3x3 matrices, with det A=9 and det B = - 6. Use properties of determinants to complete parts (a) through (e) below. a. Compute det AB. det AB = (Type an integer or a fraction.) b. Compute det 5A. det 5A = (Type an integer or a fraction.) c. Compute det BT. det BT = (Type an integer or a fraction.) d. Compute det A-7. - 1 det A (Type an integer or a simplified fraction.) e. Compute det A3. det Aº =(Type an integer or a fraction.)

Answer 1

Given |A|=9, 131=-6 a) det (AB) we have det (MB) -(det A)x(det(B)) => LAIXIBI = IABI ..det AB = 9X(-6) =-54 det AB = -54 b) det SA we have det (CA)= (^ det h where his ordes of matrix Isal det 5 A= 5x det A = 53X1A) =53x9 = 125x9 = 1125 det SA= 1125 ( det BT we have det (AT) = det A indet BT = det =-6. > LATI= IAL i.det BT = -6 d) det at we have det (A) = Tet 1nl1=1 TAI det Al- det A 9 iodet At=1 9 CS Scanned with CamScanner

e) det A² We have det An = (det A)" - IABI= LAIM det A3 = (deta)} = q3 = 729 det A3 = 729 = 1A3| CS Scanned with CamScanner