2007-6.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	6	IB 2007 Linear Algebra	4.II.10G	2007

(i) State and prove the Cayley-Hamilton theorem for square complex matrices.

(ii) A square matrix $A$ is of order $n$ for a strictly positive integer $n$ if $A^{n}=I$ and no smaller positive power of $A$ is equal to $I$.

Determine the order of a complex $2 \times 2$ matrix $A$ of trace zero and determinant 1 .