SOLUTION: We know that for scalars (real numbers) if ab = 0 then either a = 0 or b = 0. This is not true for matrices. Show this. Specifically, find two 2x2 matrices A and B such that AB=02

Question 854638: We know that for scalars (real numbers) if ab = 0 then either a = 0 or b = 0. This is not true for matrices. Show this. Specifically, find two 2x2 matrices A and B such that AB=02 but A≠02 and B≠02 (Remember 02 is the 2x2 zero matrix). This has very important consequences. It means that if we factor a matrix equation as (X − C)(X − D) = 0 then we cannot conclude that X = C or X = D. Thus, quadratic matrix equations cannot be solved by factoring. Matrices of this type are called zero divisors.)

02 is supposed to be 0 with a subscript of 2, so like the 2 in H2O. It wouldnt let me type it like that.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I can write by typing "0[2]" wrapped in triple curly brackets like }}}.

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