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Question

If A=⎡⎢⎣0121233a1⎤⎥⎦ and A−1=⎡⎢⎣1/21/21/2−43c5/2−3/21/2⎤⎥⎦, then the values of a and c are equal to

A
1,1
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B
1,1
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C
1,2
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D
1,1
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Solution

The correct option is B 1,1
A=0121233a1 and A1=1/21/21/243c5/23/21/2
Here, |A|=1(8)+2(a6)=2a4
adjA=CT=23a8a62a163121T
adjA=23a2a11862a631
Hence, A1=12a423a2a11862a631
Comparing with given A1,
12a4=12
a=1
Also, 22a4=c
c=1
Thus the values of a and c are 1 and 1 respectively.

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