First slide

Transpose of matrix

Question

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

Moderate

A

1
B

3
C

0
D

None of these

Solution

Since the matrix A is orthogonal
A′A = AA′ = I_n
⇒ |A′A| = |AA′| = |I_n|
⇒ |A′| |A| = 1
⇒ |A| |A| = 1
or |A|² = 1
$∴$ |A| = ±1

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