3. Prove that the set of matrices of the form 1 x y 01 2 0 0 1, is a group under ordinary matrix multiplication. This gr

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3 Prove That The Set Of Matrices Of The Form 1 X Y 01 2 0 0 1 Is A Group Under Ordinary Matrix Multiplication This Gr 1 (22.51 KiB) Viewed 14 times

3. Prove that the set of matrices of the form 1 x y 01 2 0 0 1, is a group under ordinary matrix multiplication. This group is known as the Heisenberg group, and is an important tool in the theory of quantum me- chanics. Is this group abelian? Why or why not? 4. Prove that in GL2 (R), det (AB) = det(A) det (B). Then, prove that this fact implies the closure of the binary operation in the group GL2(R).