If S= [ array lll 0 & 1 & 1 1 & 0 & 1 1 & 1 & 0 array ] and A= 1 2 [ array lll b+c & c-a & b-a c-b & c+a & a-b b-c & a-c & a+b array ] , then SAS ⁻¹=

Step-by-step solution

S ⁻¹= 1 2 [ array ccc -1 & 1 & 1 1 & -1 & 1 1 & 1 & -1 array ] (obtainded from matrix ' S ') Consider SA = 1 2 [ array ccc 0 & 2 a & 2 a 2 ~b & 0 & 2 ~b 2 c & 2 c & 0 array ] Hence SAS ⁻¹=( SA ) S ⁻¹ = 1 4 [ array ccc 4 a & 0 & 0 0 & 4 b & 0 0 & 0 & 4 c array ]= [ array lll a & 0 & 0 0 & b & 0 0 & 0 & c array ]