Question 1

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

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Question 1 If A and B are invertible matrices of order 3, |๐ด| = 2, |(๐ด๐ต)^(โˆ’1) | = โ€“ 1/6 . Find |๐ต| Theory We know that A A-1 = I So, |A A-1| = |I| |A A-1| = 1 |A| |A-1| = 1 |A| = 1/|๐ด^(โˆ’1) | Given |๐ด| = 2, |(๐ด๐ต)^(โˆ’1) | = โ€“ 1/6 We know that |(๐ด๐ต)^(โˆ’1) | = 1/(|๐ด๐ต|) |(๐ด๐ต)^(โˆ’1) | = 1/|๐ด||๐ต| โˆ’1/6 = 1/(2 ร— |๐ต| ) 2 ร— |๐ต| = โ€“6 |๐ต| = (โˆ’6)/2 |๐‘ฉ| = โ€“ 3

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.