Special Types of Determinants

Define skew symmetric determinant. Give one example of skew symmetric determinant of order $3\times 3$

Define symmetric determinant. Give one example of symmetric determinant of order $3\times 3$

Give one example of skew symmetric determinant of order $3\times 3$

Give one example of symmetric determinant of order $3\times 3$

Find the determinant of circulant matrix $\left[\begin{array}{cc}1& 3\\ 3& 1\end{array}\right]$.

Show that subtraction of two circulant matrices is also circulant by taking an example.

Show that addition of two circulant matrices is also circulant by taking an example.

Find the determinant of circulant matrix $\left[\begin{array}{ccc}2& 3& 4\\ 4& 2& 3\\ 3& 4& 2\end{array}\right]$.

Find the determinant of circulant matrix $\left[\begin{array}{ccc}1& 2& 3\\ 3& 1& 2\\ 2& 3& 1\end{array}\right]$

Cotyledons are also called-

If $a,b,c$ are non-zero real numbers, then$\left|\begin{array}{ccc}bc& ca& ab\\ ca& ab& bc\\ ab& bc& ca\end{array}\right|$ vanishes, when