Inverse Matrix

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If A is an invertible matrix, then (A⁻¹)⁻¹ equals

RankGuru · Accepted Answer

1. **Concept**: The inverse operation undoes itself.
2. **Formal Logic**: Let $B = A^{-1}$. By definition of an inverse, $B \cdot A = I$ and $A \cdot B = I$. This second equation ($A \cdot B = I$) establishes that **$A$ is the inverse of $B$**.
3. **Substitution**: Replacing $B$ with $A^{-1}$, we find that the inverse of $A^{-1}$ is **$A$**.

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Inverse Matrix

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