The development of broadcast regulation in the U.S. followed a logical progression:

• Early radio (post-1920): Anyone could build and operate a radio station, leading to hundreds of unlicensed stations fighting for limited frequencies and even engaging in “power wars” to drown out competitors
• Radio Act of 1927: Created the Federal Radio Commission (FRC) to organise the licensing of transmitters and assign radio station frequencies
• Communications Act of 1934: Reorganised the FRC into the Federal Communications Commission (FCC), which expanded regulatory authority to include telephone and telegraph as well as broadcasting

The driving force behind regulation was the entry of commercial advertising money and corporate interests — once radio became profitable, the government had strong incentives to impose order. The FCC's regulatory powers later expanded to include television.

The product of upper-triangular matrices $\begin{pmatrix}1&k\\0&1\end{pmatrix}$ gives $\begin{pmatrix}1&\sum k\\0&1\end{pmatrix}$.

$\sum_{k=1}^{n-1}k = \dfrac{(n-1)n}{2} = 78 \Rightarrow n(n-1)=156 \Rightarrow n=13$

The inverse of $\begin{pmatrix}1&n\\0&1\end{pmatrix} = \begin{pmatrix}1&13\\0&1\end{pmatrix}$ is $\begin{pmatrix}1&-13\\0&1\end{pmatrix}$.