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If A= [ array ll 3 & 4 1 & 2 array ] , then A⁻¹ equal to

Options

  1. A[ array cc 3 & -4 -1 & 2 array ]
  2. B[ array cc 3 2 & -2 -1 2 & 1 array ]
  3. C[ array cc 2 & -4 -1 & 3 array ]
  4. D[ array cc 1 & -2 -1 2 & 3 2 array ]

Correct answer

D. [ array cc 1 & -2 -1 2 & 3 2 array ]

Step-by-step solution

We have, A= [ array ll 3 & 4 1 & 2 array ] aligned & |A|=3 2-1 4=6-4=2 adj A= & [ array cc 2 & -4 -1 & 3 array ] & [ If A= [ array ll a & b c & d array ], then adj A= [ array cc d & -b -c & a array ] ] aligned Hence, A⁻¹= 1 |A| adj A A⁻¹= 1 2 [ array cc 2 & -4 -1 & 3 array ]= [ array cc 1 & -2 - 1 2 & 3 2 array ]

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