The determinant of a singular matrix is 0.

Explanation:

A singular matrix is defined as a square matrix that does not have an inverse. The determinant of such a matrix is always zero because:

1. A matrix is singular if its rows (or columns) are linearly dependent, meaning one or more rows can be written as a linear combination of others.
2. Linear dependence causes the determinant to equal zero, as the volume of the parallelepiped defined by its rows or columns collapses to zero.

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Related Questions:

1. How do you calculate the determinant of a matrix?
2. What is the significance of the determinant in solving linear equations?
3. How can we determine if a matrix is singular without computing the determinant?
4. What does it mean for rows or columns to be linearly dependent?
5. How does the determinant relate to eigenvalues of a matrix?

Tip:

When determining if a matrix is singular, check if any row or column can be expressed as a combination of others—it saves time compared to directly calculating the determinant!