Chapter 2 - Matrix Algebra - Supplementary Exercises - Page 163: 17

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Suppose A be a 6x4 matrix and B a 4x6 matrix. Because B has more columns than rows, its six columns are linearly dependent and there is a nonzero $x$ such that $B x=0$. Thus $A B x=A O=0 .$ This shows that the matrix $A B$ is not invertible, by the IMT.