Evaluate :

Expanding along the second row

⇒ |A| = sinβ (cosα×cosα sinβ + sinα × sinα sinβ) + cosβ (cosα cosβ × cosα + sinα×sinα cosβ) – 0

|A| = sin² β (cos²α + sin²α) + cos²β (cos²α + sin²α)

|A| = sin² β (1) + cos²β (1)

|A| = sin² β + cos²β

|A| = 1