Let's take a general case:
\(\displaystyle \begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}\)
They are asking if you square it, then you get a zero matrix.
Upon doing so, we get:
\(\displaystyle \begin{bmatrix}a^{2}+bd+cg&ab+be+ch&ac+bf+ci\\ad+de+fg&bd+e^{2}+fh&cd+ef+fi\\ag+dh+gi&bg+eh+hi&cg+fh+i^{2}\end{bmatrix}\)
Now, each of these must equal 0. Use some imagination and see if you can do that. For instance,
\(\displaystyle a^{2}+bd+cg=0\) along with the others.
There may be some thereom I am not aware of that makes this easy. I don't know.
