Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 2B / Solution

Let $P_B,P_{B^{\prime }},P_C,P_{C^{\prime }}$ have the corresponding basis vectors as columns in standard coordinates. From the PDF,The matrix representation of a linear map in standard coordinates is $P_{C}A{P}_B^{-1}$. The change of basis formula therefore givesMultiplication yields

Solved by gpt-5.6-sol high.