The n×n -matrix with min (i, j) as its ij entry is the so-called MIN matrix of the set{1,2,...,n} .In fact, this particular matrix is, up to a positive scalar, the covariance matrix of a stochastic process with increments which possess the same variance and are uncorrelated. This same matrix has also been studied by R. Bhatia [?], as he gives six different proofs for its positive definiteness. Similarly, the MAX matrix of the set{1,2,...,n} is the n× n matrix with max (i, j) as its ij entry. It turns out that MIN and MAX matrices are rather simple special cases of so-called meet and join matrices, and the theory developed for meet and join matrices can easily be applied to MIN and MAX matrices. We will learn how to factorize MIN and MAX matrices and we shall also obtain formulas for the determinants and inverses of these matrices. And finally, we are going to see the reason why every real and positive Hadamard power of a MIN matrix is always positive definite, but every real and positive Hadamard power of a MAX matrix is indefinite. What makes this presentation interesting from a students point of view is that many of the results may be obtained by only using elementary methods and techniques. For example, the determinants of MIN and MAX-matrices may be calculated quite easily by making use of the Gauss-Jordan elimination process.