Consider the matrix A=(11−11)A = \begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix}A=(1−111). What is det(An)\det(A^n)det(An)?
2n2^n2n
(2)n(\sqrt{2})^n(2)n
2n/22^{n/2}2n/2
111