Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:

(a) 4Β  Β  Β  Β  Β  Β  Β (b) 8Β 
(c) 64Β  Β  Β  Β  Β  Β (d) 16

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 28 Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is: (a) 4 (b) 8 (c) 64 (d) 16 Given A2 = 2A Taking Determinant both sides |𝑨^𝟐 | = |2𝐴| |𝑨 Γ— 𝑨| = |2𝐴| |𝐴||𝐴| = |πŸπ‘¨| Since order of matrix is 3, using|π‘˜π΄|=π‘˜^𝑛 |𝐴| |𝐴||𝐴| = 𝟐^πŸ‘ |𝑨| |𝐴||𝐴| = 8|𝐴| |𝐴||𝐴| βˆ’ 8|𝐴| = 0 |𝐴| (|𝐴|βˆ’"8" ) = 0 Thus, |𝑨| = 0 or |𝑨| = 8 Given that A is a non-singular matrix, ∴ |𝑨| = 8 Now, |πŸπ‘¨| = 𝟐^πŸ‘ |𝑨| = 8 Γ— 8 = 64 So, the correct answer is (C)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.