Thread: Linear algebra proof.

Question:
Let be the n x n matrix defined by and if . Show that if B is any n x n matrix, then .

My work:
is not zero only when , as would become . Therefore, since and . Hence, .

What step am I missing? Although it is a relatively simple proof, I am still quite new at proof-writing. Thanks in advance.

The " " is meaningless- it is certainly not what you mean. Also that "=>" indicates that something leads from one to the other. You need to say what that "something" is, not just indicate it.

You know, of course, that if C= AB then . Use the fact that if to reduce that sum to a single term.