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Two rings are said to be Morita equivalent if their categories of (left) modules are equivalent. The notion is also used in more general contexts when certain categories of representations are equivalent.

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Is it true that $A$ is Morita equivalent with $M_I(A)$ [closed]

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\i …
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