Question

If \( A \in R_{n \times n} \) and \( \det A = 0 \), then :
A. \(A\) is non singular and the rows and columns of \(A\) are linearly independent
B. \(A\) is non-singular and the rows and columns of \(A\) are linearly dependent
C. \(A\) is non-singular and \(A\) has one zero row
D. \(A\) is singular
E. \(A\) is singular and rows and columns of \(A\) are linearly dependent Choose the correct answer from the options given below :

• A. A only
• B. A and E only
• C. B and C only
• D. D only

Hint:

Remember the most important determinant property: \[ \det(A)=0 \iff A \text{ is singular} \] and \[ \det(A)\neq0 \iff A \text{ is non-singular} \] Singular matrices always contain linearly dependent rows or columns.

Answer 1

The Correct Option is D