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Are the following statements true or false? If A is an n by n square matrix. a. If A...

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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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Posted (Answer #1)

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(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.

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