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Question: let c4 x 4 matrices a such that aa ...

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Let C-4 x 4 matrices A such that A,A )} a) Show that if A, B E L then AB E AL b) Show that if A E C then A-1E L c) Suppose Sally declares herself to be at the center of the universe, and sets her watch to 0. In physics, this is an example of an event. By definition then, this event occurred at time 0, and position 0- (0,0,0), according to Sally. This information can be encoded as a vector O in Suppose sometime later, a bolt of lightning strikes a house. This is another event which Sally records as happening at time t, and Cartesian coordinates (r, y, z) This information can be encoded as a vector V in IR4. The spacetime-displacement between these events is v The space-time interval between events O and y is defined to be s = vTTy Evaluate s

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