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Question 1 If for a square matrix 𝐴,□( ) 𝐴.( adj 𝐴)=[■(2025&0&0@0&2025&0@0&0&2025)], then the value of |𝐴|+|𝑎𝑑𝑗𝐴| is equal to: (A) 1 (B) 2025+1 (C) (2025)^2+45 (D) 2025+(2025)^2Given 𝐴.( adj 𝐴)=[■(2025&0&0@0&2025&0@0&0&2025)] Taking 2025 common 𝐴.( adj 𝐴)=2025[■(1&0&0@0&1&0@0&0&1)] 𝑨.( adj 𝑨)=𝟐𝟎𝟐𝟓𝑰 And, we know that 𝑨.( adj 𝑨)=|𝑨|𝑰 Thus, |𝑨| = 2025 Finding |adj (A)| |adj (A)| = |A|n − 1 Where n is the order of matrix Since I is of order 3 × 3, therefore n = 3 Thus, |adj (A)| = |A|3− 1 = |A|2 = (2025)2 Now, |𝐴|+|𝑎𝑑𝑗𝐴| = 2025 + (2025)2 So, the correct answer is (D)

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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.