Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:

(a) 4             (b) 8 
(c) 64           (d) 16

Slide72.JPG

Advertisement

Slide73.JPG

Advertisement

Slide74.JPG

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

Transcript

Question 28 Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is: (a) 4 (b) 8 (c) 64 (d) 16 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 Given that A is a non-singular matrix, โˆด |๐‘จ| = 8 Now, |๐Ÿ๐‘จ| = ๐Ÿ^๐Ÿ‘ |๐‘จ| = 8 ร— 8 = 64 So, the correct answer is (C)

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.