If A= [ array ccc 1 & 1 & a+1 1 & a+1 & 1 a+1 & 1 & 1 array ] is not an invertible matrix, then the sum of all the values of a is

Step-by-step solution

Given, A= [ array ccc 1 & 1 & a+1 1 & a+1 & 1 a+1 & 1 & 1 array ] A is non-invertible matrix. aligned & |A|=0 & 1(a+1-1)-(1-a-1)+(a+1) (1-(a+1)^2 )=0 & a+a+a+1-(a+1)^3=0 & 3 a+1-a^3-1-3 a^2-3 a=0 & -a^3-3 a^2=0 -a^2(a+3)=0 & a=0,-3 aligned Sum of all values of a=0+(-3)=-3