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Lesson eLearning

If $det (A B) = 12$ and $det (A) = 3$ , find $det (B)$ . Give your answer as a single integer.

medium 2 marks Class 12 · Mathematics · Determinants

Answer

Determinant of B = 4

The correct answer is Determinant of B = 4 — State the final result.

Step-by-step solution

Recall the property $det (A B) = det (A) \cdot det (B)$ for square matrices of the same order.
Substitute the known values: $12 = 3 \times det (B)$ .
Solve for $det (B)$ by dividing both sides by 3: $det (B) = 12/3 = 4$ .
State the final result.

Common mistake: Adding the determinants instead of multiplying them.

Concept tested: Multiplicative property of determinants

Published 8 September 2026 · How this solution was prepared and checked

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