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Exercise 6

Avg difficulty 2.5

Suppose that AA and BB are 5×55\times5 matrices such that det⁡(A)=−2\det(A) = -2 and det⁡(B)=5\det(B) = 5. Find the following determinants:

  1. det⁡(2A)\det(2A).

  2. det⁡(A3)\det(A^3).

  3. det⁡(AB)\det(AB).

  4. det⁡(−A)\det(-A).

  5. det⁡(AB−1)\det(AB^{-1}).

Austin, Understanding Linear Algebra, §3.4 Determinants, Exercise 6

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.