If A = [ array cc 2 a & -3 ~b 3 & 2 array ] and A adj A = AA ^ T , then 2 a+3 b is

Step-by-step solution

aligned & A= [ array cc 2 a & -3 b 3 & 2 array ] & A adj A= [ array cc 2 a & -3 b 3 & 2 array ] [ array cc 2 & 3 b -3 & 2 a array ] & = [ array cc 4 a+9 b & 0 0 & 9 b+4 a array ] & A A^T= [ array cc 2 a & -3 b 3 & 2 array ] [ array cc 2 a & 3 -3 b & 2 array ] & = [ array cc 4 a^2+9 b^2 & 6 a-6 b 6 a-6 b & 13 array ] & A adj A = A A ^ T & [ array cc 4 a+9 b & 0 0 & 4 a+9 b array ]= [ array cc 4 a^2+9 b^2 & 6 a-6 b 6 a-6 b & 13 array ] & a = b and 4 a +9 ~b =13 & a = b =1 & 2 a+3 b=5 & aligned