Question 20 (Choice 1) - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

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

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

Transcript

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 × 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

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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.

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