Is it true that $A$ is Morita equivalent with $M_I(A)$ self-induced

Let $A$ be a unital Banach algebra. Is it true that $A$ is Morita equivalent with $M_I(A)$, where $I$ and $J$ beis an arbitrary index sets, and $P$ be a $J \times I$ nonzero matrix over $A$ such that $\parallel P \parallel_\infty= \{\parallel P_{ij} \parallel:i,j \in I\} \leq 1$. Letset $LM(A,P)$ be($M_I(A)$ is the vector space of all $I \times J$$I*I$ matrices $\textit{B}$ over $A$ such that $\parallel B \parallel_1=\sum _{i\in I, j\in J} \parallel A_{i,j} \parallel < \infty$. Then it is easy to check that $LM(A,P)$ with the product $X \circ Y=XPY$, $X,Y \in LM(A,P)$ and the $\ell^1$-norm is a Banach algebra that we call theentries in $\ell^1$--Munn algebra$A$. WhenLet $I=J$$a,b\in M_I(A)$ and $P$ is the identitybe an invertible $J \times J$$I*I$ matrix overwith entries in $A$, we denote $LM(A,P)$ by $M_J(A)$. Gronbaek proved that if $cl(A^2)=A$, then $M_n(A) \otimes_{M_n(A)} M_n(A)\simeq M_n(A \otimes_{A} A)$. Is this true where $n$ replaced by $J$? Since The product of $A$ is unital it$a,b$ is clear thatdefined by $cl(A^2)=A$$a.b=aPb$).

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Is it true that $A$ is Morita equivalent with $M_I(A)$ self-induced

Let $A$ be a unital Banach algebra. Is it true that $A$ is Morita equivalent with $M_I(A)$, where $I$ is anand $J$ be arbitrary index set sets, and $P$ be a ($M_I(A)$ is$J \times I$ nonzero matrix over $A$ such that $\parallel P \parallel_\infty= \{\parallel P_{ij} \parallel:i,j \in I\} \leq 1$. Let $LM(A,P)$ be the vector space of all $I*I$$I \times J$ matrices with entries in$\textit{B}$ over $A$ such that $\parallel B \parallel_1=\sum _{i\in I, j\in J} \parallel A_{i,j} \parallel < \infty$. LetThen it is easy to check that $a,b\in M_I(A)$$LM(A,P)$ with the product $X \circ Y=XPY$, $X,Y \in LM(A,P)$ and the $\ell^1$-norm is a Banach algebra that we call the $\ell^1$--Munn algebra. When $I=J$ and $P$ be an invertibleis the identity $I*I$$J \times J$ matrix with entries in over $A$, we denote $LM(A,P)$ by $M_J(A)$. The product of Gronbaek proved that if $a,b$ is defined$cl(A^2)=A$, then $M_n(A) \otimes_{M_n(A)} M_n(A)\simeq M_n(A \otimes_{A} A)$. Is this true where $n$ replaced by $a.b=aPb$)$J$? Since $A$ is unital it is clear that $cl(A^2)=A$.