Use partitioned matrices to prove by induction that for n = 2, 3,...., the n × n matrix A shown below is invertible and B is its inverse.

For the induction step, assume A and B are (k + 1) × (k + 1) matrices, and partition A and B in a form
similar to that displayed in Exercise 25.

Data from in Exercise 25

Use partitioned matrices to prove by induction that the product of two lower triangular matrices is also lower triangular.

A = B = 00 1 1 0 1 1 1 1 0 1 -1 - 1 0 1 1 0 0 0 1 0 0 0 1 0 0 -1 1