It is shown that for positive real numbers $ 0<\lambda_{ 1}<\dots<\lambda_{ n}$, $\left[\frac{ 1}{ \beta({ \lambda_i}, { \lambda_j})}\right]$, where $ \beta(\cdot,\cdot)$ denotes the beta function, is infinitely divisible and totally positive. For $ \left[\frac{ 1}{ \beta({ i},{ j})}\right]$, the Cholesky decomposition and successive elementary bidiagonal decomposition are computed. Let $\mathfrak w(n)$ be the $n$th Bell number. It is proved that $\left[\mathfrak w(i+j)\right]$ is a totally positive matrix but is infinitely divisible only upto order $4$. It is also shown that the symmetrized Stirling matrices are totally positive.
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