Matrices and Determinants
Properties of Determinants
JEE Main 2022
Grade 12
Question:
If $A$ and $B$ are square matrices of the same order, then $|AB|$ equals:
(1) $|A| + |B|$
(2) $|A + B|$
(3) $|B| |A|^{-1}$
(4) $|A| |B|$
Step-by-Step Solution
Key Concept: This is the multiplicative property of determinants — recall how the determinant of a product of two square matrices of the same order relates to the individual determinants.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)