I am asked:
Let $n$ be a positive integer, let $I = \{1, 2, 3, . . . , n\}$ and let $A$ be the $n \times n$ matrix whose entry in row $i$ and column $j$ for each $i, j \in I$ is equal to $\frac12\bigl(1+(-1)^{i+j}\bigr)$. Evaluate the permanent of $A$.
Actually evaluating a permanent for a $2\times2$ or $3\times3$ matrix is pretty easy. However I am completely lost how to evaluate a matrix $\frac12\bigl(1+(-1)^{i+j}\bigr)$.
Can someone provide some guidance on how to start this problem?