Are the following statements true or false? If A is an n by n square matrix.
a. If A is the inverse of B then A and B commute.
b. If the span of the rows of A is R^n then A is invertible.
c. An invertible matrix A can be written as a product of elementary matrices in a unique way.
(a) It is true
(b) It is true
(c) False because
They depend on how we do the row reduction.
A is invertible , its inverse is B .
By def of inverse
A and B commute.