Is the set of all diagonal 3x3 matrices a subspace of M3x3???

Question

in M3x3 the 3x3 should be a subscript. please explain your answer!

Answer 1

What is M3x3? The set of all 3x3 matrices?
Use the definition of a subset.
A is a subset of B if for every element a in A, a is also in B.

In your case, A is the set of all diagonal 3x3 matrices. Let a be an element of A. Then a is a diagonal 3x3 matrix. Since a is 3x3 matrix, a is in M3x3 also. Therefore the set of all diagonal 3x3 matrices is a subset of M3x3.

Answer 2

it depends on the angle