AP EAMCET202022 Sep 2020Evening ShiftMathematicsMatricesActual
Let A be a square matrix of order 3 . Choose the correct option regarding the following statements I. There exists a matrix B of order 3 such that A B=I₃ II. There exists a matrix C of order 3 such that C A=I₃ III. A is invertible
Options
- AOnly III implies I and II
- BI, II and III are equivalent statements
- CIn I and II, B can be different from C
- DNone of the above
Correct answer
B. I, II and III are equivalent statements
Step-by-step solution
Since, given statement (I) A B=I₃ B=I₃ A⁻¹ B=A⁻¹ Statement (II) C A=I₃ C=I₃ A⁻¹ C=A⁻¹ Statement(II) From Eqs. (i) and (ii), A is invertable matrix Given Statements (I), (II), (III) are equivalent Hence, option (2) is correct.