Chapter 2 - Matrices and Systems of Linear Equations - 2.8 The Invertible Matrix Theorem I - Problems - Page 189: 5

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The equation $$Ax = 0$$ $$Bx=0$$ has only the trivial solution $x = 0$ Consider $$(AB)x=0$$ $$A(Bx)=0$$ $$\rightarrow Bx=0$$ $$\rightarrow x=0$$ Hence, the linear equation $$(AB)x=0$$ has only the trivial solution. From the equivalence of $(a)$ and $(c)$ in the Invertible Matrix Theorem, AB is an invertible matrix.