(n x n) Matrix multiplying itself with its inverse to form the (n x n) identity matrix

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Is it ok to say Matrix A, with it's inverse, form the Identity Matrix?

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If $A$ is an $n\times n$ matrix and $\det A\ne0$ then $A\cdot A^{-1}=I_n$ where $I_n$ is the $n\times n$ identity matrix. This is the definition of the inverse of a matrix. What matrix $B$ (the inverse of $A$) do I need in order for $A\cdot B=I$.