inverse matrix

Question

A matrix A has an inverse if and only if

RankGuru · Accepted Answer

1. **Singular vs Non-singular**: A matrix with determinant equal to zero is called 'Singular' and has no inverse.
2. **Invertibility Condition**: For a matrix $A$ to be invertible, it must be **non-singular**, meaning **$|A| 
eq 0$**.
3. **Reason**: The formula for the inverse involves dividing by the determinant: $A^{-1} = \frac{1}{|A|} adj(A)$. If $|A|=0$, the expression is undefined.

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