Let . Show that G is a group under matrix multiplication.

Chapter 2, Problem 52E

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Let \(G=\left\{\left[\begin{array}{ll}a & a \\ a & a\end{array}\right] \mid a \in \mathbf{R}, a \neq 0\right\}\). Show that G is a group under matrix multiplication. Explain why each element of G has an inverse even though the matrices have 0 determinants. (Compare with Example 10.)

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