Matrices and Determinants
Singular Matrices
JEE Main 2018
Grade 12
Question:
A square matrix $A$ is said to be singular if and only if $|A|$ equals:
(1) $0$
(2) $1$
(3) $-1$
(4) any non-zero number
Step-by-Step Solution
Key Concept: Recall the defining criterion that links a square matrix's invertibility to its determinant — a singular matrix is precisely one that fails this invertibility test.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)