Question 1
If A and B are invertible matrices of order 3, |A| = 2, |(AB) ^{ -1 } | = – 1/6. Find |B|
Last updated at Oct. 1, 2019 by Teachoo
Question 1
If A and B are invertible matrices of order 3, |A| = 2, |(AB) ^{ -1 } | = – 1/6. Find |B|
Transcript
Question 1 If A and B are invertible matrices of order 3, |๐ด| = 2, |(๐ด๐ต)^(โ1) | = โ 1/6 . Find |๐ต| Theory We know that A A-1 = I So, |A A-1| = |I| |A A-1| = 1 |A| |A-1| = 1 |A-1| = 1/|๐ด| Just for reference, no need to write Given |๐ด| = 2, |(๐ด๐ต)^(โ1) | = โ 1/6 We know that |(๐ด๐ต)^(โ1) | = 1/(|๐ด๐ต|) |(๐ด๐ต)^(โ1) | = 1/|๐ด||๐ต| โ1/6 = 1/(2 ร |๐ต| ) 2 ร |๐ต| = โ6 |๐ต| = (โ6)/2 |๐ฉ| = โ 3
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