If A= [ array ll 2 & 3 1 & 2 array ], B= [ array ll 1 & 0 3 & 1 array ] , then B ⁻¹ ~A ⁻¹=

Step-by-step solution

(A) We have A= [ array ll 2 & 3 1 & 2 array ] |A|=4-3=1 A⁻¹ exists. B= [ array ll 1 & 0 3 & 1 array ] |B|=1 B⁻¹ exists aligned A⁻¹ &= [ array cc 2 & -3 -1 & 2 array ] and B⁻¹= [ array cc 1 & 0 -3 & 1 array ] B⁻¹ A⁻¹ &= [ array cc 1 & 0 -3 & 1 array ] [ array cc 2 & -3 -1 & 2 array ] &= [ array cc 2+0 & -3+0 -6-1 & 9+2 array ]= [ array cc 2 & -3 -7 & 11 array ] aligned