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

If A is a square matrix of order 3 such that 𝐴 2 = 2𝐴, then find the value of |A|.

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If A is a square matrix of order 3 such that A^2 = 2A, then find

Question 20  (Choice 1) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

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Question 20 (Choice 1) If A is a square matrix of order 3 such that 𝐴2 = 2𝐴, then find the value of |A|. 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

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