Question

If determinant of a matrix is zero, then matrix is: ____.

• A. Identity
• B. Singular
• C. Symmetric
• D. Orthogonal

Hint:

Think of "Singular" as "Single/Lonely" because it cannot find an inverse "partner." If $|A| = 0$, then $A^{-1} = \frac{1}{|A|} adj(A)$ becomes undefined due to division by zero.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Matrices are classified based on the value of their determinant, which indicates whether the matrix is invertible or "squashes" space into a lower dimension.

Step 2: Detailed Explanation:
1. Singular Matrix: A square matrix whose determinant is exactly zero ($|A| = 0$). These matrices do not have an inverse. 2. Non-Singular Matrix: A square matrix whose determinant is non-zero ($|A| \neq 0$). These are invertible. 3. Identity Matrix: Always has a determinant of 1. 4. Orthogonal Matrix: Always has a determinant of $\pm 1$.

Step 3: Final Answer:
A matrix with a zero determinant is a Singular matrix.