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An n n matrix is said to be orthogonal if AAT = ATA = In ; that is, if AT = A 1. (It turns

Annnmatrix is said to beorthogonalifAAT=ATA=In; that is, ifAT=A1. (It turns out that in two or three dimensions, the orthogonal matrices describe rotations and reflections.) Suppose thatT:R3R3is a linear transformation with standard matrixA andAis orthogonal. Show thatTpreserves volume: ifSR3is a solid with volumeV, thenT(S)also has volumeV.

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