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True or False - and Why?
a) A $3 \times 3$ real matrix need not have any real eigenvalues.
b) If an $n \times n$ matrix $A$ is invertible, then it is diagonalizable.
c) If $A$ is a $2 \times 2$ matrix both of whose eigenvalues are 1 , then $A$ is the identity matrix.
d) If $\vec{v}$ is an eigenvector of the matrix $A$, then it is also an eigenvector of the matrix $B:=A+7 I$.
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