An example question asks me to determine $[T]_{\beta}^\gamma$ where $\beta,\ \gamma$ are standard ordered bases of $\mathbb{R}^n$ and $\mathbb{R}^m$ respectively, of $T_1: \mathbb{R}^n \rightarrow \mathbb{R}^n,\ \ T_1(a_1, a_2, ...a_n) = (a_1, a_1, a_1,....., a_1)$ and also of $T_2: \mathbb{R}^n \rightarrow \mathbb{R}^n,\ \ T_2(a_1, a_2, ...a_n) = (a_n, a_{n-1}, a_{n-2},....., a_1)$
I understand that in $T_1$, $T$ needs to be an $n\times n$ matrix consisting of ones in the first column and nowhere else. In the second one, I can deduce that the ones must be on the negative diagonal.
My problem is, I don't know how I can formally present that as a solution to $[T]_{\beta}^\gamma$