Check sibling questions

Question 1

If A and B are invertible matrices of order 3, |A| = 2, |(AB) -1 | = – 1/6. Find |B|

If A and B are invertible matrices of order 3,|A| = 2, |(AB)-1| = -1/6

Question 1 - CBSE Class 12 Sample Paper for 2019 Boards - Part 2


Transcript

Question 1 If A and B are invertible matrices of order 3, |𝐴| = 2, |(𝐴𝐡)^(βˆ’1) | = – 1/6 . Find |𝐡| Theory We know that A A-1 = I So, |A A-1| = |I| |A A-1| = 1 |A| |A-1| = 1 |A-1| = 1/|𝐴| Just for reference, no need to write Given |𝐴| = 2, |(𝐴𝐡)^(βˆ’1) | = – 1/6 We know that |(𝐴𝐡)^(βˆ’1) | = 1/(|𝐴𝐡|) |(𝐴𝐡)^(βˆ’1) | = 1/|𝐴||𝐡| βˆ’1/6 = 1/(2 Γ— |𝐡| ) 2 Γ— |𝐡| = –6 |𝐡| = (βˆ’6)/2 |𝑩| = – 3

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.