aligned & A( , )= [ array ccc & & 0 - & & 0 0 & 0 & e^ array ] & [A( , )]⁻¹= aligned

Step-by-step solution

aligned & Given, A( , )= [ array rcc & & 0 - & & 0 0 & 0 & e^ array ] & Now, |A( , )|=e^ ( ^2 + ^2 )=e^ & C₁₁=e^ , C₁₂=e^ , C₁₃=0 & C₂₁=-e^ , C₂₂=e^ , C₂₃=0 & C₃₁=0, C₃₂=0, C₃₃= ^2 + ^2 =1 & adj (A( , ))= [ array ccc e^ & -e^ & 0 e^ & -e^ & 0 0 & 0 & 1 array ] & [A( , )]⁻¹= 1 e^ e^ [ array ccc & - & 0 & & 0 0 & 0 & e^ - array ] & = [ array ccc & - & 0 & & 0 0 & 0 & e^ - array ]=A(- ,- ) aligned