# Math Help - Linear algebra. Showing n x n matrix has no inverse

1. ## Linear algebra. Showing n x n matrix has no inverse

If A is an n x n matrix, where n is an odd integer, which satisfies A^T=-A (ie its skew-symmetric). Show that A has no inverse...........i can understand why but i cant show it mathematically

2. Note that $\det(^tA)=\det(A)$ and $\det(aA)=a^n\det(A)$.
Now, applying the determinant in the equality we have
$\det(^tA)=(-1)^n\det(A)\Rightarrow \det(A)=-\det(A)\Rightarrow 2\det(A)=0\Rightarrow\det(A)=0$