Question

The rank of \(3 \times 3\) matrix \(A\) is 2. The determinant of the matrix is

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

A square matrix has a non-zero determinant only if its rank is equal to its order.

Answer 1

The Correct Option is A

Step 1: Understand the concept of rank and determinant. 
The rank of a matrix is the maximum number of linearly independent rows (or columns). If a \(3 \times 3\) matrix has rank less than 3, its rows (or columns) are linearly dependent. 
Step 2: Relation between rank and determinant. 
If the rank of a square matrix is less than its order (here, less than 3), then its determinant is zero.