Let $A$ be an $m$ by $m$ matrix and $B$ an $r$ by $r$ matrix and let Diag$(A,B)$ be a block diagonal matrix. It is an $(m+r)$ by $(m+r)$ matrix where the top left $m$ by $m$ corner is $A$, the bottom right $r$ by $r$ corner is $B$ and $0$ else where.
I am trying to explain to first year students that $\det$Diag$(A,B)$ = $\det A \cdot \det B$. I was wondering if someone could assist me with how I can explain to them in a clear manner (other than just giving an example or two)? Thank you!