If A is a square matrix of order 3 such that ๐ด 2 = 2๐ด, then find the value of |A|.

 

Slide2.JPG

Slide3.JPG

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

Transcript

Question 20 (Choice 1) If A is a square matrix of order 3 such that ๐ด2 = 2๐ด, then find the value of |A|. Given A2 = 2A Taking Determinant both sides |๐‘จ^๐Ÿ | = |2๐ด| |๐‘จ ร— ๐‘จ| = |2๐ด| |๐ด||๐ด| = |๐Ÿ๐‘จ| Since order of matrix is 3, using|๐‘˜๐ด|=๐‘˜^๐‘› |๐ด| |๐ด||๐ด| = ๐Ÿ^๐Ÿ‘ |๐‘จ| |๐ด||๐ด| = 8|๐ด| |๐ด||๐ด| โˆ’ 8|๐ด| = 0 |๐ด| (|๐ด|โˆ’"8" ) = 0 Thus, |๐‘จ| = 0 or |๐‘จ| = 8

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.