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
- AI
- B( 0 )
- C( ( 2 I )
- 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 )