Answer: [[3,-5],[-1,2]].
- A [[3,-5],[-1,2]]
- B [[-3,5],[1,-2]]
- C [[3,5],[-1,-2]]
- D [[2,5],[1,3]]
Correct answer: A. [[3,-5],[-1,2]]
Explanation: det(A) = 6-5 = 1. adj([[2,5],[1,3]]) = [[3,-5],[-1,2]]. A<sup>-1</sup> = [[3,-5],[-1,2]]/1 = [[3,-5],[-1,2]]. Check: [2,5][3,-5] = 6-5=1, [2,5][-1,2] = -2+10=8... verify row1*col1: 2*3+5*(-1)=1. Row1*col2: 2*(-5)+5*2=0. Correct.
Concept context
Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.