   Chapter 1.6, Problem 21E

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# Suppose that A is an invertible matrix over ℝ and O is a zero matrix. Prove that if A X = O , then X = O .

To determine

To prove: Let A is an invertible matrix over and O is a zero matrix. If AX=O, then X=O.

Explanation

Given information:

A is an invertible matrix over and O is a zero matrix.

Formula used:

If AMm×n(), then AOn×p=Om×p.

Proof:

Let A is an invertible matrix over and O is a zero matrix.

Therefore, AA1=A1A=I

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