We study a class of ` p -matrix algebras, namely LMp I (C). We show that LMp I (C) is pseudo-contractible if and only if the index set I is finite. Also,pseudoamenability of LMp I (C) is investigated. For a subclass of ` p -matrix algebras, say ` p -upper triangular algebras Amenability, approximate biprojectivity and approximate biflatness are discussed here, where 1 ≤ p ≤ 2.