A= [ array lll 0 & 1 & 2 1 & 2 & 3 3 & a & 1 array ] and A⁻¹= 1 2 [ array ccc 1 & -1 & 1 -8 & 6 & 2 c 5 & -3 & 1 array ] , then values of a and c are respectively

Step-by-step solution

We know that AA ⁻¹=1 aligned & [ array lll 0 & 1 & 2 1 & 2 & 3 3 & a & 1 array ] [ array ccc 1 2 & -1 2 & 1 2 -4 & 3 & c 5 2 & -3 2 & 1 2 array ]= [ array ccc 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] & [ array ccc 1 & 0 & c +1 0 & 1 & 2+2 c 4-4 a & 3 a -3 & 2+ ac array ]= [ array ccc 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] aligned Thus c +1 c =-1 and 4-4 a =0 a =1