Let A= [a_ i j ] be 3 3 matrix such that A [ array l 0 1 0 array ]= [ array l 0 0 1 array ], A [ array l 4 1 3 array ]= [ array l 0 1 0 array ] and A [ array l 2 1 2 array ]= [ array l 1 0 0 array ] , then a₂₃ equals :

Step-by-step solution

aligned & Let A= [ array lll a & b & c d & e & f g & h & i array ] & [ array lll a & b & c d & e & f g & h & i array ] [ array l 0 1 0 array ]= [ array l 0 0 1 array ] & b=0, e=0, h=1 & and [ array lll a & 0 & c d & 0 & f g & 1 & i array ] [ array l 4 1 3 array ]= [ array l 0 1 0 array ] & . array l 4 a+3 c=0 4 d+3 f=1 4 g+1+3 i=0 array ....(1) aligned aligned & and [ array ccc a & 0 & c d & 0 & f g & 1 & i array ] [ array l 2 1 2 array ]= [ array l 1 0 0 array ] & . array c 2 a+2 c=1 2 d+2 f=0 2 g+1+2 i=0 array ..