In Exercises 13 - 18, use the fact that ifa b d - bA = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c aeach matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 2 3A = - 1 2

Matrix inversion is the process of finding a matrix A^(-1) such that when it is multiplied by the original matrix A, the result is the identity matrix I. For a 2x2 matrix, the formula for the inverse is A^(-1) = 1/(ad-bc) * [d, -b; -c, a], where 'a', 'b', 'c', and 'd' are the elements of the matrix. The determinant (ad-bc) must be non-zero for the inverse to exist.

The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix. For a 2x2 matrix, the determinant is calculated as ad - bc. A non-zero determinant indicates that the matrix is invertible, while a zero determinant means the matrix does not have an inverse.

The identity matrix is a special type of square matrix that acts as the multiplicative identity in matrix multiplication. For a 2x2 matrix, the identity matrix I_2 is represented as [1, 0; 0, 1]. When a matrix A is multiplied by its inverse A^(-1), the result is the identity matrix, confirming that A^(-1) is indeed the correct inverse.