If Adj⎡⎢⎣102−11−2021⎤⎥⎦=⎡⎢⎣5a−2110−2−2b⎤⎥⎦,then[ab]=
A
[−41]
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B
[−4−1]
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C
[41]
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D
[4−1]
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Solution
The correct option is C[41] Let A=⎡⎢⎣102−11−2021⎤⎥⎦
We know that AdjA=CT
where C=Co-factor matrix of A C=⎡⎢⎣1−(−4)−(−1)−2−0−(0−4)1−0−(2−0)0−2−(−2+2)1−0⎤⎥⎦ =⎡⎢⎣51−241−2−201⎤⎥⎦
Now CT=⎡⎢⎣54−2110−2−21⎤⎥⎦=AdjA ⇒a=4,b=1