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Groups and FieldsEasyGroups and the Group Axioms

Groups and the Group Axioms · Easy problem

Let C=(1201)C=\begin{pmatrix}1&2\\0&1\end{pmatrix} and D=(1031)D=\begin{pmatrix}1&0\\3&1\end{pmatrix} under matrix multiplication. Using the law (CD)−1=D−1C−1(CD)^{-1}=D^{-1}C^{-1}, find the sum of the four entries of (CD)−1(CD)^{-1}.