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Direction: Consider the following for the next 02 (two) items:

Let A and B be (3 × 3) matrices with det A = 4 and det B = 3

What is det (2AB) equal to?

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NDA (Held On: 21 Apr 2019) Maths Previous Year paper
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  1. 96
  2. 72
  3. 48
  4. 36

Answer (Detailed Solution Below)

Option 1 : 96
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Detailed Solution

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Concept:

If A and B are square matrices of order n, then det (m × AB) = mn × det (A) × det (B) where m ∈ R is a scalar.

Calculation:

Given: A and B be (3 × 3) matrices with det A = 4 and det B = 3

As we know that, if A and B are square matrices of order n, then det (m × AB) = mn × det (A) × det (B) where m ∈ R is a scalar.

⇒ det (2AB) = 23 × det (A) × det (B) = 8 × 4 × 3 = 96.

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