Let . Show that G is a group under matrix multiplication. Explain why each element of G...

Let . 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.)

Reference:

EXAMPLE 10 The set of all 2 × 2 matrices with real entries is not a group under the operation defined in Example 9. Inverses do not exist when the determinant is 0.