Question

What happens if the determinant of a $3\times 3$ matrix is $0$?

Answer 1

Property of determinant:

When the determinant of a $3\times 3$ matrix is zero:

1. The rows and columns are linearly dependent vectors.
2. The matrix is not invertible.
3. The system of linear equations is linearly dependent. The system has infinitely many solutions.

Hence, some effects of $\left|A\right|=0$,is explained.