Determinant of odd matrix Given a matrix $A = \{{a_{i,j}}\} \in M_{7\times7}(\Bbb R)$ 
It is said that
$a_{i,j} = 0$ if $i$,$j$ are both odd.
Show that $det(A) = 0$
Any hints?

Let $e_1,\dots,e_7$ denote the standard basis of $\Bbb R^7$. Let $P$ be the permutation matrix
$$
P = \pmatrix{e_1&e_3&e_5&e_7&e_2&e_4&e_6}
$$
Then $PAP^T$ can be written in the form
$$
M = P^TAP = \pmatrix{0_{4 \times 4} & M_{12}\\M_{21}&M_{22}}
$$
$M_{21}$ is $3 \times 4$, so it has linearly dependent columns.
