Decomposing an inner product of matrices into outer products

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In a lecture on bayesian reasoning and active learning I came across a slide that seemed to imply that the inner product of a matrix X (of n rows and d columns) with itself could be decomposed into the sum of outer products of row vectors xi (from 1 to n). My question is two-fold:

  1. Is this true?
  2. If it is what is the proof?