Recall that for an m x n matrix A, the transpose A T of A is the
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Recall that for an m x n matrix A, the transpose AT of A is the matrix whose jth column is the jth row of A. Show that if A is an m x n matrix such that ATA is invertible, then the projection matrix P = A(ATA)-1AT is an idempotent in the ring of n x n matrices.
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