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The set of all 2x2 matrices with real entries and determinant 1 forms a group under matrix multiplication. Which of the following is the identity element of this group?
The matrix [[1, 0], [0, 1]]
The matrix [[1, 2], [3, 4]]
The matrix [[2, 1], [1, 2]]
The matrix [[0, 1], [1, 0]]
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