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.

Am I correct?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.

__________________________________________________ ______________

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