First slide

Applications of determinant

Question

The inverse of a skew symmetric matrix of odd order is

Moderate

A

A symmetric matrix
B

A skew symmetric matrix
C

diagonal matrix
D

does not exist

Solution

Let A be a skew symmetric matrix of order n.
By definition $A' = - A$
$\begin{array}{l} \Rightarrow |A^{'}| = | - A | \\ \Rightarrow | A | = (- 1)^{n} | A | \\ \Rightarrow | A | = - | A | [∵ n is odd] \end{array}$
$\Rightarrow 2 | A | = 0$
$\Rightarrow | A | = 0. ∴ A^{- 1} does not exist .$

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