a) If matrix B is similar to matrix A. Show that both matrices have the same determinant, that is ( operatorname{det}(B)= operatorname{det}(A) ). (Hint: Use the definition ( mathrm{B}= mathrm{P}^{-1} mathrm{AP} ) ) (5 marks)

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a) If matrix B is similar to matrix A. Show that both matrices have the same determinant, that is  (  operatorname{det}(B)= operatorname{det}(A)  ). (Hint: Use the definition  (  mathrm{B}= mathrm{P}^{-1}  mathrm{AP}  ) ) (5 marks)

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