Question
If [ array cc 1 & - \\ & 1 array ] [ array cc 1 & \\ - & 1 array ]^ -1 = [ array cc a & -b \\ b & a array ], then
BITSAT
Mathematics
Matrices
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. a=1, b=1
- B. a= 2 , b= 2
- C. a= 2 , b= 2
- D. None of these
Answer
C. a= 2 , b= 2
Step-by-step solution
Given, [ array cc 1 & - \\ & 1 array ] [ array cc 1 & \\ - & 1 array ]^ -1 = [ array cc a & -b \\ b & a array ] [ array cc 1 & - \\ & 1 array ] 1 1+ ^2 [ array cc 1 & - \\ & 1 array ] = [ array cc a & -b \\ b & a array ] 1 1+ ^2 [ array cc 1- ^2 & -2 \\ 2 & 1- ^2 array ]= [ array cc a & -b \\ b & a array ] [ array cc 1- ^2 1+ ^2 & 2 1+ ^2 \\ 2 1+ ^2 & 1- ^2 1+ ^2 array ]= [ array cc a & -b \\ b & a array ] [ array cc 2 & - 2 \\ 2 & 2 array ]= [ array cc a & -b \\ b & a array ] a= 2 , b= 2
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