Is the zero matrix diagonalizable?
Then for any invertible matrix $P$, we can say $P^{-1}\cdot 0 \cdot P=0$ ?
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$\begingroup$The zero-matrix is diagonal, so it is certainly diagonalizable.
$\endgroup$ $\begingroup$The definition of a diagonal matrix is that it must have zeros everywhere except on its diagonal. This is true for the zero matrix. So the zero matrix is a diagonal matrix. By the definition of matrix multiplication $$P^{-1}\cdot 0 \cdot P = 0$$ is true for any invertible matrix.
$\endgroup$ 1 $\begingroup$What is the result of $P^{-1} \cdot 0$? What is the product of that with $P$?
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