JEE Main2014MathematicsMatricesActual
If A is a 3 × 3 non-singular matrix such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals, where X ' denotes the transpose of the matrix X .
Options
- AB - 1
- BB - 1 '
- CI + B
- DI
Correct answer
D. I
Step-by-step solution
A ' = A T A A ' = A ' A B = A - 1 A ' B ' = A - 1 A ' ' = A ' ' · A - 1 ' = A A - 1 ' B B ' = A - 1 A ' · A A - 1 ' = A - 1 · A · A ' · A - 1 ' ∵   A A ' = A ' A = I · A ' · A - 1 ' = I · A - 1 A ' ∵   C D ' = D ' C ' = I · I ' = I 2 ∵   I = I ' = I