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The product of a 2x5 matrix P and a 5x3 matrix B shall be a 2x3 zero matrix. P and B are all matrices of integers.

P = [6 2 -5 -6 1;3 6 1 -6 -5]

One possible B is [0 -4 0;3 0 0;-1 -1 3;2 -3 -2;1 1 3]

This solution B has a property: det(PP^{t}) = det(B^{t}B) = 7778

The question is: What does this property mean? How to get another B with this property?

Senmeis

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# Why this property of the product of two matrices

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