Question

If A and B are invertiable matrices of the same order such that I (AB)^-1 I = 8 , If I A I =2 then I B I is ​

Answer 1

Explanation:

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Answer 2

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FORMULA TO BE IMPLEMENTED

1.

$\: \implies \displaystyle \: | {A}^{ - 1} | = \frac{1}{ | A | } \:$

2.

$| \: AB\: | \: = | \:A \: | | B |$

GIVEN

A and B are invertible matrices of the same order such that

$|{ (AB)}^{ - 1}| = 8 \: \: and \: \: \: |A \: | = 2$

TO DETERMINE

$| \: B\: |$

CALCULATION

$|{ (AB)}^{ - 1}| = 8$

$\implies \displaystyle \: \frac{1}{ | AB | } \: = 8$

$\implies \displaystyle \: \frac{1}{ | A || B | } \: = 8$

$\implies \displaystyle \: \frac{1}{ 2|B | } \: = 8$

$\implies \displaystyle \: { | B | } \: = \frac{8}{2} = 4$