inverse matrix

Question

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 **$A$**.

Rank Guru

inverse matrix

Select the correct option:

More inverse matrix Practice Questions

The inverse of matrix A = [[2, 3], [1, 2]] is

A matrix A has an inverse if and only if