Thanks for your responses. It took me a while to decipher your notation. (@graphking, I think it will take me another week to decipher your comment, thank you)
I pasted the question from the textbook so I think it is accurately reproduced here. The book is "An introduction to linear algebra" by...
Textbook answer:
"If P1P2 = P2P1 then S is contained in T or T is contained in S."
My query:
If P1 = \begin{pmatrix}
1 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{pmatrix}and P2 =\begin{pmatrix}
0 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 0 \\
\end{pmatrix}
as far as I...