If A= [ array ccc 2 & 1 & 3 -1 & 2 & 0 4 & 1 & 3 array ], B= [ array lll 3 & 2 & 1 1 & 2 & 3 3 & 1 & 0 array ] , then det (2 B⁻¹ A⁻¹ ) is equal to

Step-by-step solution

(d) aligned A & = [ array ccc 2 & 1 & 3 -1 & 2 & 0 4 & 1 & 3 array ], B= [ array lll 3 & 2 & 1 1 & 2 & 3 3 & 1 & 0 array ] A⁻¹ & = 1 |A| adj A, B⁻¹= 1 |B| adj B |A| & =2(6)-1(-3)+3(-1-8),|B|=4 & =12+3-27=-12 aligned aligned adj A & = [ array ccc 6 & 0 & -6 3 & -6 & -3 -9 & 2 & 5 array ], adj B= [ array ccc -3 & 1 & 4 9 & -3 & -8 -5 & 3 & 4 array ] A⁻¹ & = [ array ccc -1 / 2 & 0 & 1 / 2 -1 / 4 & 1 / 2 & 1 / 4 3 / 4 & -1 / 6 & -5 / 12 array ], B⁻¹ & = [ array ccc -3 / 4 & 1 / 4 & 1 9 / 4 & -3 / 4 & -2 -5 / 4 & 3 / 4