Annulus amplitude of FZZT branes revisited

We revisit the annulus amplitude of FZZT branes with general matter sectors (r,s) using the recent development of matrix model and minimal Liouville gravity. Following the boundary description of the 1-matrix model and bulk resonance transformation between primary operators we find the consistency of the brane decomposition into (1,1)-branes. We also investigate the corresponding results obtained directly from the minimal Liouville gravity and demonstrate the perfect agreement with the matrix results.