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Problem 7 IMC 2004 Macedonia

Source:

July 26, 2004
linear algebramatrixalgebrapolynomiallimitIMCcollege contests

Problem Statement

Let AA be a real 4×24\times 2 matrix and BB be a real 2×42\times 4 matrix such that AB=(10−10010−1−10100−101). AB = \left(% \begin{array}{cccc} 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & -1 \\ -1 & 0 & 1 & 0 \\ 0 & -1 & 0 & 1 \\ \end{array}% \right). Find BABA.
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