If the product of the matrix B= [ array ccc 2 & 6 & 4 1 & 0 & 1 -1 & 1 & -1 array ] with a matrix A has the inverse C= [ array ccc -1 & 0 & 1 1 & 1 & 3 2 & 0 & 2 array ] , then A⁻¹ equals

Step-by-step solution

(B A)⁻¹=C (given) or A⁻¹ B⁻¹=C or A⁻¹ [ array ccc 2 & 6 & 4 1 & 0 & 1 -1 & 1 & -1 array ]⁻¹= [ array ccc -1 & 0 & 1 1 & 1 & 3 2 & 0 & 2 array ] Multiply by B on both sides, we get A⁻¹ (B⁻¹ B )= [ array ccc -1 & 0 & 1 1 & 1 & 3 2 & 0 & 2 array ] [ array ccc 2 & 6 & 4 1 & 0 & 1 -1 & 1 & -1 array ] or A⁻¹= [ array ccc -3 & -5 & -5 0 & 9 & 2 2 & 14 & 6 array ]_ 3 3