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

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Transcript

Question 1 If A and B are invertible matrices of order 3, |𝐴| = 2, |(𝐴𝐵)^(−1) | = – 1/6 . Find |𝐵| 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, |(𝐴𝐵)^(−1) | = – 1/6 We know that |(𝐴𝐵)^(−1) | = 1/(|𝐴𝐵|) |(𝐴𝐵)^(−1) | = 1/|𝐴||𝐵| −1/6 = 1/(2 × |𝐵| ) 2 × |𝐵| = –6 |𝐵| = (−6)/2 |𝑩| = – 3

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.