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

The rest of the post is locked. Join Teachoo Black to see the full post.


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)

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.