Question: Example 1.4 shows that the only matrix similar to a zero matrix is itself and that the only matrix similar to the identity is itself.

Example 1.4 shows that the only matrix similar to a zero matrix is itself and that the only matrix similar to the identity is itself.
(a) Show that the 1 × 1 matrix whose single entry is 2 is also similar only to itself.
(b) Is a matrix of the form cI for some scalar c similar only to itself?
(c) Is a diagonal matrix similar only to itself?

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a Because the matrix 2 is 11 the matrices P and P 1 are also 11 and ... View full answer

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