To calculate absorption probabilities and the expected number of steps to absorption in a Markov chain, you first identify the absorbing states (where the process ends) and transient states (where the process may move but does not terminate). For the absorption probabilities, construct the fundamental matrix N=(I−Q)−1, where Q is the submatrix of the transition matrix representing transitions between transient states. The absorption probability matrix B=NR, where R represents transitions from transient to absorbing states, gives the likelihood of being absorbed into each absorbing state from any transient state. To find the expected number of steps to absorption, calculate t=N1t = N is a column vector of ones, and t provides the expected steps for each transient state. These calculations leverage matrix operations and are central to analyzing absorbing Markov chains.