If det A is close to zero, is the matrix A nearly singular? Experiment with the nearly

Question:

If det A is close to zero, is the matrix A nearly singular? Experiment with the nearly singular 4 ( 4 matrix A in Exercise 9 of Section 2.3. Compute the determinants of A, 10A, and 0.1A. In contrast, compute the condition numbers of these matrices. Repeat these calculations when A is the 4 ( 4 identity matrix. Discuss your results?