Determine whether the statement is true or false. Justify your answer.
1. Multiplication of an invertible matrix and its inverse is commutative.
2. When the product of two square matrices is the identity matrix, the matrices are inverses of one another.
3. Explain how to determine whether the inverse of a 2 × 2 matrix exists, as well as how to find the inverse when it exists.
4. Explain how to write a system of three linear equations in three variables as a matrix equation AX = B, as well as how to solve the system using an inverse matrix.