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KCET2016MathematicsMatrices

If ( A = 1 [ array ll ⁻¹( x ) & ⁻¹ ( x ) ⁻¹ ( x ) & ⁻¹( x ) array ] B = [ array cc - ⁻¹( x ) & ⁻¹ ( x ) ⁻¹ ( x ) & - ⁻¹( x) array ] ) then ( A - B ) equal to

Options

  1. AI
  2. B( 0 )
  3. C( ( 2 I )
  4. D( 1 2 I )

Correct answer

D. ( 1 2 I )

Step-by-step solution

We have, (A= [ array ll 1 ⁻¹(x ) & 1 ⁻¹ ( x ) 1 ⁻¹ ( x ) & 1 ⁻¹( x) array ] B= [ array cc - 1 ⁻¹(x ) & 1 ⁻¹ ( x ) 1 ⁻¹ ( x ) & - 1 ⁻¹( x) array ] ) ( A-B= [ array ll 1 ( ⁻¹ x + ⁻¹ x ) & 1 ( ⁻¹ x - ⁻¹ x ) 1 ( ⁻¹ x - ⁻¹ x ) & 1 ( ⁻¹ x )+ ⁻¹ x array ] ) ( [ array cc 1 2 & 0 0 & 1 2 array ] [ array l ⁻¹ x+ ⁻¹ x= 2 and ⁻¹ x+ ⁻¹ x= 2 array ] ) (= 1 2 [ array ll 1 & 0 0 & 1 array ]= 1 2 I )

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