First, we need to find the inverse of matrix A, which is [[2,3],[2,4]].
The formula for the inverse matrix of a 2x2 matrix
```
[[a, b],
[c, d]]
```
is
```
1/(ad - bc) * [[d, -b],
[-c, a]].
```
Using this formula, we can find the inverse of matrix A :
The determinant `ad - bc` for matrix A is `(2*4) - (3*2) = 8 - 6 = 2`.
So the inverse of matrix A is:
1/2 * [[4, -3],
[-2, 2]]
= [[2, -1.5],
[-1, 1]].
This is the inverse of matrix A. Now, we will use this inverse to solve for x in the equation `Ax = B`.
We are given that B is [[18,13],[22,18]], and the formula to find x is `x = A^(-1)B`.
Applying matrix multiplication to `A^(-1)B`:
[[2, -1.5],
[-1, 1]]
*
[[18,13],
[22,18]]
= [[3, -1],
[4, 5]].
Hence the solution matrix x is [[3, -1], [4, 5]]. This is the solution to the matrix equation.