Question

What is the necessary condition for a matrix A to be invertible?

• A. |A|=|Adj A|
• B. |A|=|A^T|
• C. |A|≠0
• D. A ≠ 0

Answer 1

The correct option is C

|A|≠0

Invertibility of a matrix is one of its major properties. If a matrix is invertible it’s also called non-singular. The necessary condition for this is $|A|\ne 0$.

You can understand this from the definition of inverse of a matrix. The expression for obtaining the inverse is, $A^{-1}=\frac{1}{|A|}.Adj\left(A\right)$

Here for the denominator not to become zero the inequality $|A|\ne 0$ should be satisfied. Hence the required condition.