Let A= [ array cc 1 & 2 -2 & 1 array ] and B⁻¹= [ array ll 1 & 1 0 & 2 array ] . If (A B⁻¹ )⁻¹= [ array ll a & b c & d array ] , then 2 b+5 c+10 d=

Step-by-step solution

A B⁻¹= [ array cc 1 & 2 -2 & 1 array ] [ array ll 1 & 1 0 & 2 array ]= [ array cc 1 & 5 -2 & 0 array ] Now, |A B⁻¹ |=0-(-10)=10 and adj (A B⁻¹ )= [ array cc 0 & -5 2 & 1 array ] (A B⁻¹ )⁻¹= 1 |A B⁻¹ | adj (A B⁻¹ ) [ array ll a & b c & d array ]= 1 10 [ array cc 0 & -5 2 & 1 array ]= [ array cc 0 & - 1 2 1 5 & 1 10 array ] aligned & a=0, b=- 1 2 , c= 1 5 , d= 1 10 & 2 b+5 c+10 d=-1+1+1=1 aligned