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Question: linear algebra all parts if possible if not part c...

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Linear algebra

All parts if possible, IF NOT (part C and D)
Please give an explanation as well!

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6. Matriz Multiplication: Let M and N be matrices and N- (e CL M = and v the vector If we first apply N and then M to v we obtain the vector MN (a) Show that the composition of matrices MN is also a linear oper- ator (b) Write out the components of the matrix product MN in terms of the componnts of M and the components of N. Hint: use the general rule for multiplying a 2-vector by a 2x2 matrix. (c) Try to answer the following common question, Is there any sense in which these rules for matrix multiplication are uavoidable, or are they just a notation that could be replaced by some other notation? (d) Generalize your multiplication rule to 3 × 3 matrices
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