[Solved] What Is Det (2AB) Equal To?

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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. Download Solution PDF Share on Whatsapp