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Question

If A−1=⎡⎢⎣10−2−210−110⎤⎥⎦, then which of the following options are correct?

A
|A|=2
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B
adj(A)=⎢ ⎢ ⎢1201112012120⎥ ⎥ ⎥
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C
|adj(A)|=4
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D
A=12
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Solution

The correct options are
B A=12
D adj(A)=⎢ ⎢ ⎢1201112012120⎥ ⎥ ⎥
We are given A1=∣ ∣102210110∣ ∣
A1=2(2+1)=2
We check all the options
A. |A|=1A1=12
B. adj(A)=A1|A|=12∣ ∣102210110∣ ∣=∣ ∣ ∣ ∣1201112012120∣ ∣ ∣ ∣
C. |adj(A)|=1(12+14)=14
D. A=|A|=12
B,D are correct

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