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

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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 × 𝑨| = |2𝐴| |𝐴||𝐴| = |𝟐𝑨| Since order of matrix is 3, using|𝑘𝐴|=𝑘^𝑛 |𝐴| |𝐴||𝐴| = 𝟐^𝟑 |𝑨| |𝐴||𝐴| = 8|𝐴| |𝐴||𝐴| − 8|𝐴| = 0 |𝐴| (|𝐴|−"8" ) = 0 Thus, |𝑨| = 0 or |𝑨| = 8 Given that A is a non-singular matrix, ∴ |𝑨| = 8 Now, |𝟐𝑨| = 𝟐^𝟑 |𝑨| = 8 × 8 = 64 So, the correct answer is (C)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.