If  B=52α1021α3−1 is the inverse of a  3×3 matrix A, then the sum of all values of α  for which det(A)+1=0, is

Given matrix B is the inverse matrix of 3×3 matrix A,  Where B=52α1021α3−1We know that ,detA=1detB           ∵detA−1=1detASince, det(A) +1=01det⁡(B)+1=0⇒det⁡(B)=−1⇒5(−2−3)−2α(0−α)+1(0−2α)=−1⇒−25+2α2−2α=−1⇒2α2−2α−24=0⇒α2−α−12=0⇒(α−4)(α+3)=0⇒α=−3,4 So, required sum of all values of α is 4−3=1