Prove that the set of matrices of the form I 1 2 0 is a group...

   

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Prove that the set of matrices of the form I 1 2 0 is a group under matrix multiplication. This group, known as the Heisenberg group, is important in quantum physics. Matrix multiplication in the Heisenberg group is defined by 1 1 y z' 6 : 9 6 : 9 - 67 *). 0 0 1 1 0 0 1 0 0 1 1 0 1 2+2 0 0 Prove that the set of matrices of the form I 1 2 0 is a group under matrix multiplication. This group, known as the Heisenberg group, is important in quantum physics. Matrix multiplication in the Heisenberg group is defined by 1 1 y z' 6 : 9 6 : 9 - 67 *). 0 0 1 1 0 0 1 0 0 1 1 0 1 2+2 0 0