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added the BA tag since I expect the OP is thinking about a BA notion of Morita equivalence
Yemon Choi
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Is it true that $A$ is Morita equivalent with $M_I(A)$

Let $A$ be a unital Banach algebra. Is it true that $A$ is Morita equivalent with $M_I(A)$, where $I$ is an arbitrary index set ($M_I(A)$ is the space of $I*I$ matrices with entries in $A$. Let $a,b\in M_I(A)$ and $P$ be an invertible $I*I$ matrix with entries in $A$. The product of $a,b$ is defined by $a.b=aPb$).