# 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...

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.

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### 1 Answer

(a) It is true

(b) It is true

(c) False because

They depend on how we do the row reduction.

Explanation (a)

A is invertible , its inverse is B .

By def of inverse

`AB=BA=I_n`

A and B commute.