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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Let A , B , and C be elements of M 2 ( ) , where A is not a zero matrix. Prove or disprove that A B = A C implies B = C .

To determine

If A,B, and C be elements of M2(), where A is not a zero matrix, then check whether AB=AC implies B=C or not.

Explanation

Given information:

A,B, and C be elements of M2(), where A is not a zero matrix.

Formula used:

Definition: Matrix multiplication

The product of m×n matrix A over and n×p matrix B over is m×p matrix C=AB, where the element cij in row i and column j of AB is found by using the elements in row i of A, and the elements in column j of B in the following manner:

columnjofBcolumnjofCrowiofA[ai1ai2ai3ain][b1jb2jb3jbnj]=[cij]rowiofC

Where cij=ai1b1j+ai2b2j++ainbnj

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