$$\begin{matrix} 1 & 0 & 0\\ 0 & 0.5 & 0.5\\ 0 & 0.5 & 0.5 \end{matrix}$$
Given that this is a right transition matrix, would you call the state in the first row, say A, an absorbing state?
An absorbing state requires that it cannot be left, which A fulfills. However, it does not communicate with other states, thus no other state can enter it. So, is it still an absorbing state since the full definition of an absorbing state is that it is a state that once entered cannot be left.