If A= [ array cc 2 & -1 -1 & 3 array ] , then the inverse of (2 A^2+5 A ) is

Step-by-step solution

aligned A & = [ array cc 2 & -1 -1 & 3 array ] & A^2= [ array cc 2 & -1 -1 & 3 array ] [ array cc 2 & -1 -1 & 3 array ] A^2 & = [ array cc 5 & -5 -5 & 10 array ] Now, 2 A^2+5 A & =2 [ array cc 5 & -5 -5 & 10 array ]+5 [ array cc 2 & -1 -1 & 3 array ] & = [ array cc 20 & -15 -15 & 35 array ] If A & = [ array ll a & b c & d array ], then~ A⁻¹= 1 a d-b c [ array cc d & -b -c & a array ] (2 A^2+5 A )⁻¹ & = 1 475 [ array cc 35 & 15 15 & 20 array ] & = 1 95 [ array ll 7 & 3 3 & 4 array ] aligned