First slide

Transpose of matrix

Question

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

Moderate

A

1
B

-1
C

$\pm 1$
D

0

Solution

As A is an orthogonal matrix,
$\begin{array}{l} A^{'} A = A A^{'} = I_{n} \\ \Rightarrow |A^{'} A| = |A A^{'}| = |I_{n}| \\ \Rightarrow |A^{'}| | A | = 1 \Rightarrow | A | | A | = 1 \\ \Rightarrow | A |^{2} = 1 \Rightarrow | A | = \pm 1 \end{array}$

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