Final answer:
To solve for the matrix x in the equation ax(d bx)−1=c, rearrange the equation to isolate x by following the steps: multiply both sides by (d bx)-1, then multiply both sides by the inverse of d bx, and finally multiply both sides by the inverse of a.
Step-by-step explanation:
To solve for the matrix x in the equation ax(d bx)−1=c, we can rearrange the equation to isolate x. Start by multiplying both sides of the equation by (d bx)-1. This will cancel out the inverse and leave us with ax = c(d bx)-1. Next, multiply both sides by the inverse of d bx, which will cancel out the term on the right side of the equation. The final step is to multiply both sides by the inverse of a, resulting in x = c(d bx)-1(a)-1.