If A is an orthogonal matrix, then |A| is - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
1
B
-1
C
$\pm 1$
D
0

Solution:

As A is an orthogonal matrix,

$\begin{array}{l} A^{'} A = A A^{'} = I_{n} \\ \Rightarrow |A^{'} A| = |A A^{'}| = |I_{n}| \\ \Rightarrow |A^{'}| | A | = 1 \Rightarrow | A | | A | = 1 \\ \Rightarrow | A |^{2} = 1 \Rightarrow | A | = \pm 1 \end{array}$

If A is an orthogonal matrix, then $| A |$ is

Solution:

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