If A= [ array ccc 1 & 2 & 3 1 & 1 & 1 1 & -1 & 1 array ], B= [ array lll 1 & 1 & 0 0 & 1 & 3 3 & 0 & 4 array ] , C= [ array lll 2 & 0 & 1 0 & 1 & 0 3 & 2 & 1 array ] , then ( ( ((A B C)⁻¹ )^T )⁻¹ )^T=

Step-by-step solution

Given matrices A= [ array ccc 1 & 2 & 3 1 & 1 & 1 1 & -1 & 1 array ], B= [ array lll 1 & 1 & 0 0 & 1 & 3 3 & 0 & 4 array ] aligned & and C= [ array lll 2 & 0 & 1 0 & 1 & 0 3 & 2 & 1 array ] & ( ( ((A B C)⁻¹ )^T )⁻¹ )^T= ( ( (C⁻¹ B⁻¹ A⁻¹ )^T )⁻¹ )^T & = ( ( (A^T )⁻¹ (B^T )⁻¹ (C^T )⁻¹ )⁻¹ )^T= (C^T B^T A^T )^T=A B C aligned aligned & = [ array ccc 1 & 2 & 3 1 & 1 & 1 1 & -1 & 1 array ] [ array lll 1 & 1 & 0 0 & 1 & 3 3 & 0 & 4 array ] [ array lll 2 & 0 & 1 0 & 1 & 0 3 & 2 & 1 array ] & = [ array rrr 10 & 3 & 18 4 & 2