Answer
a) True
b) False
c) False
d) True
e) True
Work Step by Step
a) An $n$ x $n$ matrix $A$ is said to be invertible if there is an $n$ x $n$ matrix $C$ such that $CA = I$ and $AC = I$. (page 105)
b) $(AB)^{-1} = B^{-1}A^{-1}$ - Theorem 6 b. (page 107)
c) If $ad-bc \ne 0$, $A$ is invertible - Theorem 4. (page 105)
d) If $A$ is an invertible $n$ x $n$ matrix, then for each $\mathbf{b}$ in $\mathbb{R}^n$, the equation $A$$\mathbf{x}= \mathbf{b}$ has the unique solution $\mathbf{x} = A^{-1}\mathbf{b}$. -Theorem 5 (page 106)
e) Rule: Each element matrix $E$ is invertible. (page 109)
