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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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Prove part b of Theorem 1.35.

Theorem 1.35 Special Properties of I n

Let A be an arbitrary m × n matrix over R . With I n as defined in the preceding paragraph,

A I n = A

To determine

To prove: Let A be an arbitrary m×n matrix over . With In=[δij]n×n where δij is Kronecker delta, then AIn=A.

Explanation

Given information:

A be an arbitrary m×n matrix over . With In=[δij]n×n where δij={1ifi=j0ifij is Kronecker delta

Formula used:

Definition of 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[x

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