Exercise6

Suppose that \(A\) and \(B\) are \(5\times5\) matrices such that \(\det A = -2\) and \(\det B = 5\text{.}\) Find the following determinants:

  1. \(\det(2A)\text{.}\)

  2. \(\det(A^3)\text{.}\)

  3. \(\det(AB)\text{.}\)

  4. \(\det(-A)\text{.}\)

  5. \(\det(AB^{-1})\text{.}\)

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