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Question

If 11x1x1x11has no inverse, then the real value of x is-

A
2
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B
3
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C
0
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D
1
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Solution

The correct option is D 1
A=11x1x1x11
A1=adjA|A|
when |A|=0A1 doesn't exist.
Det A=1(x(1)(1)(1))(1)[1(1)(x)(1)]+x[1x2]
=(x+1)+[1x](1+x2)(x)
=1+x+1xxx3
2xx3=0
x3+x2=0 when x=1

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