AP EAMCET202124 Aug 2021Evening ShiftMathematicsMatricesActual
If A is a non-singular matrix such that A A^T=A^T A and B=A⁻¹ A^T , then
Options
- AA B^T=I
- BB B^T=I
- CA^T B^T=I
- DB⁻¹ B^T=I
Correct answer
B. B B^T=I
Step-by-step solution
We have, A A^T=A^T A and B=A⁻¹ A^T Now, B B^T= (A⁻¹ A^T ) (A⁻¹ A^T )^T=A⁻¹ A^T (A^T )^T (A⁻¹ )^T [ (A B)^T=B^T A^T ]=A⁻¹ A^T A (A^T )⁻¹ [ (A^T )^T=A, (A⁻¹ )^T= (A^T )⁻¹ ]=A⁻¹ A A^T (A^T )⁻¹ aligned B B^T & =I I=I B B^T & =I aligned