A square matrix $A$ is **invertible** if and only if:

Question

Accepted Answer

C. $|A| 
e 0$ (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.

Answer

$A$ is symmetric

Answer

$A$ is a diagonal matrix

Answer

The trace of $A$ is non-zero