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 August 14, 2026 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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