Let K {\displaystyle {}K} be a field, and m , n , p ∈ N {\displaystyle {}m,n,p\in \mathbb {N} } . Prove that the transpose of a matrix satisfies the following properties (where A , B ∈ Mat m × n ( K ) {\displaystyle {}A,B\in \operatorname {Mat} _{m\times n}(K)} , C ∈ Mat n × p ( K ) {\displaystyle {}C\in \operatorname {Mat} _{n\times p}(K)} , and s ∈ K {\displaystyle {}s\in K} ).
be a
field,
and
.
Prove that the transpose of a matrix satisfies the following properties (where
,
,
and
).
