MathematicsIf C is a skew symmetric of order 3. and X is a column matrix with 3 rows. then X’CX

$If C is a skew symmetric of order 3. and X is a column matrix with 3 rows. then (X^{'} C X)$

A
Null matrix
B
Number of elements in the matrix $X^{'} C X$ is one
C
column matrix with 3 rows
D
Row matrix with 3 columns

Solution:

$\begin{matrix} {(X^{'} C X)}^{'} = X^{'} C^{'} {(X^{'})}^{'} \\ = - X^{'} C X \\ And the order of the matrix X^{'} C X is 1×1 \\ Hence, X^{'} C X = O \end{matrix}$

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