Hello, all! Could somebody draw a proof-sketch of next expression from tensor algebra on matrices: determinant of tensor product $A~ \times ~B$ of $n \times n$-matrix $A$ on $m \times m$-matrix $B$ is $\det(A)^m \cdot \det(B)^n$.

Please, give me a link or reference if it is online or in some book. Thank you.

Hello, all! Could somebody draw a proof-sketch of next expression from tensor algebra on matrices over finite fields: determinant of tensor product $A~ \times ~B$ of $n \times n$-matrix $A$ over finite field $GF(q)$ on $m \times m$-matrix $B$ over finite field $GF(q)$ is $\det(A)^m \cdot \det(B)^n$.

Please, give me a link or reference if it is online or in some book. Thank you.