Are there two 3 by 3 matrices A and B, both of rank 2,such that AB is the zero matrix? Explain your answer

Question

Are there two 3 by 3 matrices A and B, both of rank 2,such that AB is the zero matrix? Explain your answer
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Solution 1

Yes, there are two 3 by 3 matrices A and B, both of rank 2, such that AB is the zero matrix. Here is the explanation:

Step 1: Understand the Rank of a Matrix The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. A 3 by 3 matrix of rank 2 means that there Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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