Page 77 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(b)
(c)

Let , , and .
10. for the matrix A in Exercise 9.
for any square matrix A.
(a) Show that

(b) Show that

Find the inverse of
11.

Find the inverse of
12.

Consider the matrix
13.

where . Show that A is invertible and find its inverse.

Show that if a square matrix A satisfies , then .
14.

15.
(a) Show that a matrix with a row of zeros cannot have an inverse.

(b) Show that a matrix with a column of zeros cannot have an inverse.

Is the sum of two invertible matrices necessarily invertible?
16.

Let A and B be square matrices such that . Show that if A is invertible, then .
17.