# Show that the product of two 2 times 2 skew symmetric matrices is diagonal. Is this true for n times n skew symmetric matrices with n > 2?

Show that the product of two $2×2$ skew symmetric matrices is diagonal. Is this true for $n×n$ skew symmetric matrices with n > 2?
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Theodore Schwartz
Step 1
Given:
Show that the product of two $2×2$ skew symmetric matrices is diagonal. Is this true for $n×n$ skew symmetric
matrices with n > 2?
Step 2
Explanation:
Since skew−symmetric matrix is of the form given below ${a}_{ij}=-{a}_{ji}$
Consider skew−symmetric matrix A and B,
$A=\left[\begin{array}{cc}0& a\\ -a& 0\end{array}\right],B=\left[\begin{array}{cc}0& b\\ -b& 0\end{array}\right]$
$AB=\left[\begin{array}{cc}0& a\\ -a& 0\end{array}\right]\left[\begin{array}{cc}0& b\\ -b& 0\end{array}\right]=\left[\begin{array}{cc}-ab& 0\\ 0& -ab\end{array}\right]$
Since product of $2×2$ skew−symmetric matrix is diagonal.Since this is only true for $n×n$ skew−symmetric matrices.where , n=2
Hence the solution.
Jeffrey Jordon
Jeffrey Jordon