A permutation $\sigma$ of $k$ elements $a_1,...,a_k$ is a one-to-one function from the set $A$ containing that elements to the same and in particular a trasposition is a permutation that swap only two elements. Now a permutation is even if an even number swappings is necessary to apply to obtain it and otherwise it is odd and in particular we say that the sign of a permutation is $1$ if it is even and it is $-1$ if the permutation is odd. So it is possible to prove that any permutation is the composition of a number $r$ of transpositions such that the quantity $(-1)^r$ is equal to the sign fo the permutation.
So if $\sigma$ is the permutation of $(k+l)$ elements that swaps the first $l$ elements of $A$ with the last ones, that is $$ \sigma(1)=k+1,...,\sigma(l)=k+l,\sigma(l+1)=1,...,\sigma(k+l)=k $$ then I ask to prove that its sign is $(-1)^{kl}$. So could someone help me, please?