alleryA square matrix $A$ is **invertible** if and only if:
A$A$ is symmetric
B$A$ is a diagonal matrix
C$|A| \ne 0$ (i.e. $A$ is non-singular)
DThe trace of $A$ is non-zero
Answer & Solution
Correct answer: C. $|A| \ne 0$ (i.e. $A$ is non-singular)
A square matrix has an inverse if and only if its determinant is non-zero.
The inverse is then given by $A^{-1} = \dfrac{1}{|A|}\operatorname{adj}(A)$.
A singular matrix ($|A| = 0$) maps some non-zero vector to zero, so it has no two-sided inverse.
Neither symmetry, diagonality, nor non-zero trace alone is sufficient.
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