mitrix algebra let A and B be 4x4 matrices with detA10 and d

mitrix algebra

let A and B be 4x4 matrices with det(A)=10 and det(B)= -3.

let Cbe the matrixe obtained from A by swapping the first and last rows .

use properties of determinants find the following:

(a) det(C )

(b) det(AB)

(c) det(-A)

Solution

(a)

Exchanging rows changes the determinant by a factor of -1

Hence,

det(C)==det(A)=-10

(b)

det(AB)=det(A)det(B)=10*(-3)=-30

(c)

det(-A)=det(-I*A)=det(-I)det(A)=-det(A)=-10