Final answer:
To check if matrix A is invertible, calculate its determinant. If non-zero, the inverse can be found using cofactors or Gaussian elimination. Matrix A can also be expressed as a product of elementary matrices if it's reducible to the identity matrix.
Step-by-step explanation:
To determine whether matrix A is invertible, we need to calculate its determinant. If the determinant is not zero, the matrix is invertible and we can find its inverse. The determinant of matrix A, which is 1 0 3 2 1 -1 2 3 3, needs to be calculated using the rule of Sarrus or a similar method.
Once the determinant is found to be non-zero, the inverse of matrix A can be calculated using cofactors and the adjugate of the matrix, or by employing Gaussian elimination.
Regarding the representation of matrix A as a product of elementary matrices, we can perform a series of row operations to reduce matrix A to the identity matrix. Each row operation corresponds to multiplication by an elementary matrix. If we can reduce A to the identity matrix, then we can express A as a product of the inverses of those elementary matrices