In this paper, we study some homological and cohomological properties of Banach algebras for some ` p-matrix algebras, say LMp I (C). We give enough and sufficient condition that LMp I (C) has a central approximate identity. Then we characterize pseudo-contractibility of LMp I (C). We prove that, for each non-epty index set I, LMp I (C) is pseudo-amenable. Also we turn our attention towards amenability, approximate biprojectivity and approximate biflatness of ` p-upper triangular algebras
