Exercise 4: Determinant properties

Given the two matrices with det(A)=3 and det(B)=-2
evaluate the following determinants:
  1. \(\det\left(AB\right)\)
  2. \(\det\left(BA\right)\)
  3. \(\det\left(3AB\right)\)
  4. \(\det\left(A^TB\right)\)
  5. \(\det\left(A^{-1}B\right)\)
Solution:
  1. 3x2 =-6
  2. -2x3 = -6
  3. 3^3*3*-2=-162
  4. 3*-2 = -6
  5. -2/3

Exercise 5: System of equations

Solve the following system of equations: