   Chapter 1.6, Problem 29E

Chapter
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Textbook Problem
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# Let A = [ a b c d ] over ℝ . Prove that if a d − b c = 0 , then A does not have an inverse.

To determine

To prove: Let A=[abcd] over and adbc=0, then A does not have an inverse.

Explanation

Given information:

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]=[<

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