(A-1)bx=ab

Solution for (A-1)bx=ab equation:

Simplifying
(A + -1) * bx = ab

Reorder the terms:
(-1 + A) * bx = ab

Reorder the terms for easier multiplication:
bx(-1 + A) = ab
(-1 * bx + A * bx) = ab
(-1bx + bxA) = ab

Solving
-1bx + bxA = ab

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-1ab' to each side of the equation.
-1bx + -1ab + bxA = ab + -1ab

Reorder the terms:
-1ab + -1bx + bxA = ab + -1ab

Combine like terms: ab + -1ab = 0
-1ab + -1bx + bxA = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(-1a + -1x + xA) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

Move all terms containing b to the left, all other terms to the right.

Simplifying
b = 0
Subproblem 2
Set the factor '(-1a + -1x + xA)' equal to zero and attempt to solve:

Simplifying
-1a + -1x + xA = 0

Solving
-1a + -1x + xA = 0

Move all terms containing b to the left, all other terms to the right.

Add 'a' to each side of the equation.
-1a + -1x + a + xA = 0 + a

Reorder the terms:
-1a + a + -1x + xA = 0 + a

Combine like terms: -1a + a = 0
0 + -1x + xA = 0 + a
-1x + xA = 0 + a
Remove the zero:
-1x + xA = a

Add 'x' to each side of the equation.
-1x + x + xA = a + x

Combine like terms: -1x + x = 0
0 + xA = a + x
xA = a + x

Add '-1xA' to each side of the equation.
xA + -1xA = a + x + -1xA

Combine like terms: xA + -1xA = 0
0 = a + x + -1xA

Simplifying
0 = a + x + -1xA

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}