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KCET2025MathematicsMatrices

If B= [ array ll 1 & 3 1 & array ] be the adjoint of a matrix A and |A|=2 , then the value of is

Options

  1. A4
  2. B5
  3. C2
  4. D3

Correct answer

B. 5

Step-by-step solution

For a (2 2 ) matrix (A ), ( adj (A)=|A| A⁻¹ A⁻¹= 1 |A| adj (A) ) So: (A⁻¹= 1 2 [ array ll 1 & 3 1 & array ] ) Now, recall for a (2 2 ) matrix: (A⁻¹= 1 det (A) [ array cc d & -b -c & a array ] ) So, comparing: ( 1 2 [ array ll 1 & 3 1 & array ]= 1 2 [ array cc d & -b -c & a array ] adj (A)= [ array cc d & -b -c & a array ] ) Matching entries: - (d=1 ) - (-b=3 b=-3 ) - (-c=1 c=-1 ) - (a= ) Now compute: (|A|=a d-b c= (1)-(-3)(-1)= -3 ) Given (|A|=2 ), so: ( -3=2 =5 )

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