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For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE. There is no need to justify your answers to this problem - but you should know either a proof or a counterexample.

a) If $A$ is an invertible $4 \times 4$ matrix, then $\left(A^{T}\right)^{-1}=\left(A^{-1}\right)^{T}$, where $A^{T}$ denotes the transpose of $A$.
b) If $A$ and $B$ are $3 \times 3$ matrices, with $\operatorname{rank}(A)=\operatorname{rank}(B)=2$, then $\operatorname{rank}(A B)=2$.
c) If $A$ and $B$ are invertible $3 \times 3$ matrices, then $A+B$ is invertible.
d) If $A$ is an $n \times n$ matrix with rank less than $n$, then for any vector $b$ the equation $A x=b$ has an infinite number of solutions.
e) ) If $A$ is an invertible $3 \times 3$ matrix and $\lambda$ is an eigenvalue of $A$, then $1 / \lambda$ is an eigenvalue of $A^{-1}$,
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