AP EAMCET202316 May 2023Morning ShiftMathematicsMatricesActual
If A= [ array lll a₁₁ & a₁₂ & a₁₃ a₂₁ & a₂₂ & a₂₃ array ] and B= [ array lll b₁₁ & b₁₂ & b₁₃ b₂₁ & b₂₂ & b₂₃ array ] , then which one of the following is True?
Options
- AA ^ T BB ^ T A = B ^ T A ~A ^ T B
- BThe orders of A^T B^T A and B^T A A^T B are equal
- CThe orders of A + B , A ^T ~B , BA ^ T are equal
- DRank of A and B are equal
Correct answer
B. The orders of A^T B^T A and B^T A A^T B are equal
Step-by-step solution
Give matrices are A= [ array lll a₁₁ & a₁₂ & a₁₃ a₂₁ & a₂₂ & a₂₃ array ] ; B= [ array lll b₁₁ & b₁₂ & b₁₃ b₂₁ & b₂₂ & b₂₃ array ] Here matrix A and B have order 2 3 . Order of A^T and B^T is 3 2 . Now, order of A_ 3 2 ^T B_ 2 3 B_ 3 2 ^T A_ 2 3 =3 3 ...(i) And order of B_ 3 2 ^T A_ 2 3 A_ 3 2 ^T B_ 2 3 =3 3 ...(ii) So, from eqn. (i) and (ii) Order of A^T B B^T A= Order of B^T A A^T B