Final answer:
The statement that a square matrix A is invertible if the matrix equation Ax=b has a unique solution is true, because the unique solution implies that the matrix has a non-zero determinant and that its columns are linearly independent.
Step-by-step explanation:
If A is an nxn square matrix and for some nx1 matrix b the matrix equation Ax=b has a unique solution, then the statement that A is invertible is true. A square matrix is invertible if and only if it has a non-zero determinant, which is equivalent to saying that its columns (or rows) are linearly independent and span the n-dimensional space. The existence of a unique solution for the equation Ax=b implies that there are no free variables or linear dependencies among the columns of A, hence its columns span the space and the determinant is non-zero, implying that A is indeed invertible.