Given that A is a square matrix of order 3 and |A|=- 2 , then |adj( 2 A)| is equal to
a) -2^6 (b) +4 (c) -2^8 (d) 2^8
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CBSE Class 12 Sample Paper for 2024 Boards
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CBSE Class 12 Sample Paper for 2024 Boards
Last updated at Aug. 14, 2023 by Teachoo
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We know that |𝒂𝒅𝒋 𝑨| = |𝑨|^(𝒏−𝟏) where n is the order of determinant ∴|𝒂𝒅𝒋 𝟐𝑨| = |𝟐𝑨|^(𝒏−𝟏) Given Order = n = 3 Now, our equation becomes |𝒂𝒅𝒋 𝟐𝑨| = |𝟐𝑨|^(𝟑−𝟏) |𝑎𝑑𝑗 2𝐴| = |2A|^2 Using property: |𝐤𝑨|=𝒌^𝒏 |𝑨|, Where n is the order of matrix |𝑎𝑑𝑗 2𝐴| = (〖𝟐^𝟑 |𝑨|)〗^𝟐 |𝑎𝑑𝑗 2𝐴| = 〖〖〖(2〗^3)〗^2 |A|〗^2 |𝒂𝒅𝒋 𝟐𝑨| = 𝟐^𝟔 〖(−𝟐)〗^𝟐 |𝑎𝑑𝑗 2𝐴| = 2^6 〖(2)〗^2 |𝒂𝒅𝒋 𝟐𝑨| = 𝟐^𝟖 So, the correct answer is (d)