Final answer:
Matrix A has an inverse if its determinant is non-zero, which cannot be determined without the specific matrix entries. For vectors A and B of equal magnitude and opposite direction, A - B has the same direction as vector A.
Step-by-step explanation:
To determine if matrix A has an inverse, we need to compute the determinant of matrix A and make sure that it is not zero. A square matrix has an inverse if and only if its determinant is not equal to zero. Unfortunately, you have not provided the specific entries of matrix A, so I cannot compute the determinant for you. Typically, if the matrix is 2x2, the determinant is ad-bc for matrix [[a, b], [c, d]]. For larger matrices, the process involves more complex calculations or using methods such as Gaussian elimination or finding the adjugate matrix. Once the determinant is found to be non-zero, the inverse can be calculated.
In the case of vectors, if vectors A and B are equal in magnitude and opposite in direction, then A - B would have the same direction as vector A. Since B is opposite to A, subtracting B (which is like adding the opposite of B) would effectively result in doubling the vector A in magnitude, pointing in the same direction as A.