A matrix `X` has `a+b` rows and `a+2` columns while the matrix `Y` has `b+1` rows and `a+3` columns. Both matrices `X Y` and `Y X` exist. Find `a` and `b` . Can you say `X Y` and `Y X` are of the same type? Are they equal.

Explanation

To solve the problem, we need to analyze the dimensions of the matrices \(X\) and \(Y\) and derive equations based on the conditions given.

### Step 1: Define the dimensions of matrices \(X\) and \(Y\)
- Matrix \(X\) has \(a + b\) rows and \(a + 2\) columns.
- Matrix \(Y\) has \(b + 1\) rows and \(a + 3\) columns.

### Step 2: Set up equations based on the existence of products \(XY\) and \(YX\)
1. For the product \(XY\) to exist, the number of columns in \(X\) must equal the number of rows in \(Y\):
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