From the invariance of the spacetime interval it follows η η = Λ Λ T η η Λ Λ and this matrix equation contains the general conditions on the Lorentz transformation to ensure invariance of the spacetime interval. Taking the determinant of the equation using the product rule gives immediately [ det ( Λ Λ ) ] 2 = 1 ⇒ ⇒ det ( Λ Λ ) = ± ± 1