First slide

Applications of determinant

Question

If nth-order square matrix A is a orthogonal, then $| adj (adj A) |$ is

Moderate

A

always -1 if n is even
B

always 1 if n is odd
C

always 1
D

none of these

Solution

Since A is orthogonal, we have
$\begin{array}{l} {AA}^{T} = I \\ or |{AA}^{T}| = 1 \\ or |A^{2}| = 1 \\ or | A | = \pm 1 \end{array}$
Now, $|adj . (adj. A)| = {|A|}^{(n - 1)^{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App