Video Transcript
True or false: A diagonal matrix does not have to be a square matrix.
In this question, we’re given a statement. And we need to determine whether this statement is true or false. So, let’s start by working out exactly what this statement is telling us. The statement says that a diagonal matrix does not have to be a square matrix. In other words, this is asking the question, is being a square matrix a requirement for being a diagonal matrix?
So, to answer this question, we’re first going to need to recall exactly what we mean by a diagonal matrix. We recall a diagonal matrix is a square matrix where all of the entries not on the main diagonal of our matrix are equal to zero. And for this question, the important thing to realize is that all diagonal matrices are square matrices. Therefore, just from this definition, we can see that our statement is false. A diagonal matrix does in fact have to be a square matrix. Therefore, we were able to show the statement given to us in the question is false. All the diagonal matrices must be square matrices .
