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If AB=[{:(4,11),(4,5):}]and A=[{:(3,2),(...

If `AB=[{:(4,11),(4,5):}]and A=[{:(3,2),(1,2):}]`, then what is the value of the determinant of the matrix B ?

A

4

B

-6

C

`-(1)/(4)`

D

-28

Text Solution

Verified by Experts

The correct Answer is:
B
Given that, `AB=[{:(4,11),(4,5):}]and A=[{:(3,2),(1,2):}]`
Let `B=[{:(a,b),(c,d):}]`
`rArr [{:(3,2),(1,2):}][{:(a,b),(c,d):}]=[{:(4,11),(4,5):}]`
`rArr [{:(3a+2c,3b+2b),(a+2c,b+2b):}]=[{:(4,11),(4,5):}]`
`rArr 3a + 2c = 4 and a + 2c = 4" "...(1)`
`and 3b + 2d = 11 and b + 2d = 5" "...(2)`
From equation set (1) a = 0 and c = 2 and from equation set (2), b = 3 and d = 1
`rArr B=[{:(0,3),(2,1):}]`
Hence `|B|=|{:(0,3),(2,1):}|=0-6=-6`
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