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