Lorentz transformations also include parity inversion P = [ 1 0 0 − − I ] which negates all the spatial coordinates only, and time reversal T = [ − − 1 0 0 I ] which negates the time coordinate only, because these transformations leave the spacetime interval invariant. Here I is the 3d identity matrix. These are both symmetric, they are their own inverses (see involution (mathematics)), and each have determinant −1. This latter property makes them improper transformations.