This paper deals with the BK-AK property of the integrated rate space ${int}{ell}_{pi}$. Importance of ${delta}^{(k)}$ in this content is pointed out. We investigate a determining set for the integrated rate space ${int}{ell}_{pi}$. The set of all infinite matrices transforming ${int}{ell}_{pi}$, into BK-AK space Y is denoted $({int}{ell}_{pi}:;Y)$. We characterize the classes $({int}{ell}_{pi}:;Y)$. When $Y={ell}_{infty},;c_0,;c,;{ell}^p,;bv,;bv_0,;bs,;cs,;{ell}_p,;{ell}_{pi}$. In summary we have the following table: