Final answer:
To solve the equation AB = BC for A, assuming that A, B, and C are square matrices and B is invertible, we can simplify the equation by multiplying both sides by the inverse of B and applying the property of the identity matrix. The solution for A is A = C.
Step-by-step explanation:
To solve the equation AB = BC for A, assuming that A, B, and C are square matrices and B is invertible, we can multiply both sides of the equation by the inverse of B. This gives us B^(-1)AB = B^(-1)BC. Since B^(-1)B is equal to the identity matrix I, we have AI = C. Therefore, the solution for A is A = C.