Can the product of two covariance matrices AB be a covariance matrix, especially if AB=BA?
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Concise Answer: No, generally AB is not a covariance matrix; however, if AB=BA, then AB could be a covariance matrix.
Detailed Explanation: The product of two covariance matrices does not necessarily yield another covariance matrix because it may not satisfy properties like symmetry or non-negative definiteness. If AB=BA, it suggests commutativity, which is a property of covariance matrices for joint Gaussian distributions, hence under specific conditions, AB could be a covariance matrix.