I have two questions for which I need help:

a] A diagonal matrix is defined as a square all of whose entries off the main diagonal are zeros. Show that the set of n * n diagonal matrices is closed under multiplication. State a rule for finding the product of the diagonal matrices.

Code:

I'd answer this by:
Let A : |a ... 0 ... 0|
|0 ... a ... 0|
|0 ... 0 ... a|
Let B : |b ... 0 ... 0|
|0 ... b ... 0|
|0 ... 0 ... b|
.:
AB = |ab ... 0 ... 0|
|0 ... ab ... 0|
|0 ... 0 ... ab|
The set of n * n matrices is therefore closed under matrix
multiplication.
As for the rule:
The product of diagonal matrices is the ith,jth value of the
first matrix, times the ith,jth value of the second matrix
along the main diagonal.

Am I correct?

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b] Let A be the square matrix and 0 the zero matrix of the

same order. Show A0 = 0A = 0.

Code:

A0, I believe means A is a zero matrix denoted by the 0. I
think 0A means 0 by A.
To solve this question, I'd say:
A0 = |0 0|
|0 0|
0A = |0 0|
|0 0|
A0 = 0A = 0