Question 1 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at February 12, 2025 by Teachoo

[Sample Paper Class 12] If for square matrix A, 𝑨. (𝒂𝒅𝒋𝑨) = 2025 - CBSE Class 12 Sample Paper for 2025 Boards

part 2 - Question 1 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 1 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

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 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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