If a matrix has determinant zero then it is singular matrix.Select one:TrueFalse

Answer

1. Understanding the Terminology:

   • A singular matrix is defined as a square matrix that does not have an inverse.

2. Determinant Insight:

   • The determinant of a matrix is a scalar value that can be calculated from its elements. A determinant of zero indicates that the matrix does not span the entire space and therefore does not have sufficient rank.

3. Connection Between Determinant and Singularity:

   • If the determinant of a matrix $A$ is zero ($\text{det}(A) = 0$), it implies that the rows (or columns) of the matrix are linearly dependent, leading to the conclusion that $A$ is singular.

4. Conclusion:

   • Thus, the statement "If a matrix has determinant zero then it is singular matrix" is indeed True.

Final Answer

True. A matrix with a determinant of zero is a singular matrix.