AP EAMCET · Maths · Matrices
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 \(A B=I_3\)
II. There exists a matrix \(C\) of order 3 such that \(C A=I_3\)
III. \(A\) is invertible
- A Only III implies I and II
- B I, II and III are equivalent statements
- C In I and II, B can be different from C
- D None of the above
Answer & Solution
Correct Answer
(B) I, II and III are equivalent statements
Step-by-step Solution
Detailed explanation
Since, given statement (I) \(A B=I_3\) \[ \Rightarrow \quad B=I_3 A^{-1} \Rightarrow B=A^{-1} \] Statement (II) \(C A=I_3 \Rightarrow C=I_3 \times A^{-1}\) \[ C=A^{-1} \] Statement(II) From Eqs. (i) and (ii), \(A\) is invertable matrix Given Statements (I), (II), (III) are…
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