If A and B are square matrices of the same order 3, such that |A|=2 and AB=2I, write the value of  |B|

 

 

 

 
 
 
 
 

Answers (1)

|AB|=|A|\cdot |B| \, \, \, \, -(1)

|kA|=k^n\cdot |A| \, \, \, \, -(2)

n\Rightarrow  order of matrix

As  AB=2I,

Taking determinant, we get

|AB|=|2I| 

|A||B|=2^3|I|      [using (1) and (2)]

2\cdot |B|=8\cdot 1       [\because |A|=2\: \: and\: \: |I|=1]

\therefore |B|=4

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