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I've attached what I have thus far and then the notes that I received back below the questions.

I need to prove A1 - A10. Some require specific numeric entries.

1/7/19 Steps are shown leading from A+0 to A. The sequence of steps is incomplete, and no justifications were evident for the steps. To begin the demonstration, it is claimed that 0 is an even integer and the zero matrix is a member of M(2Z). Sufficient justification for these claims was not evident. The notation used for the integer 0 and the zero matrix is also identical. A clear distinction is needed.

1/7/19 Steps are shown which result in a matrix B such that A+B = 0. The steps shown and the existence of such a matrix in M(2Z) have not been justified. In the work to determine the entries of B, it is unclear what steps/operations were used to conclude that "w = -a, x = -b, y = -c, z = -d". Only the defined ring operations of addition and multiplication on 2Z and M(2Z) may be used in the development.

1/7/19 A specific illustration of the additive inverse property was not evident.

1/7/19 Some steps are included that address A + (B + C) and (A + B) + C. The steps are incomplete and no justification is evident. The entries of the final matrices shown for each side, such as "𝑎 + 𝑤 + 𝑝" lack proper grouping symbols to indicate the order of operations. Once these grouping symbols are included, additional steps and justification will be necessary to reconcile the two sides.

1/7/19 A specific illustration of the additive associative property was not evident.