KCET2023MathematicsMatrices
If A= [ array cc 1 & / 2 - / 2 & 1 array ] and A B=I , then B is equal to
Options
- A^2 / 2 A
- B^2 / 2 I
- C^2 / 2 A
- D^2 / 2 A^T
Correct answer
D. ^2 / 2 A^T
Step-by-step solution
G̣iven, A= [ array cc 1 & 2 - 2 & 1 array ] and A B=I B=A⁻¹ aligned & Now A= [ array cc 1 & 2 - 2 & 1 array ] & |A|= [ array cc 1 & 2 - 2 & 1 array ]=1+ an ^2 2 = ^2 2 & adj A= [ array cc 1 & - 2 2 & 1 array ] & A⁻¹= 1 ^2 2 [ array cc 1 & - 2 2 & 1 array ] & = ^2 2 [ array cc 1 & .- 2 ] 2 & 1 array ^2 2 A T . & aligned B= [ ^2 2 ] A T