Question

If the inverse of a matrix exists, then the matrix is called:

• A. Singular
• B. Non-singular
• C. Symmetric
• D. Skew-symmetric

Hint:

Whenever you see the word “inverse”, immediately check determinant: \[ |A|\neq0 \] This is the most important condition for invertibility.

Answer 1

The Correct Option is B

Concept: A square matrix has an inverse only when its determinant is non-zero. Such matrices are called non-singular matrices. Important fact: \[ A^{-1}\text{ exists } \iff |A|\neq0 \]

Step 1: Recall the condition for existence of inverse.
For any square matrix $A$: \[ A^{-1}=\frac{1}{|A|}\text{Adj}(A) \] This formula is valid only when: \[ |A|\neq0 \]

Step 2: Interpret the determinant condition.
Matrices are classified as:
• Singular matrix: \[ |A|=0 \]
• Non-singular matrix: \[ |A|\neq0 \] Since inverse exists only when determinant is non-zero, the matrix must be non-singular. Hence, \[ \boxed{\text{Non-singular}} \]