Problem

If , then show thatwhere I denotes the 2 × 2 identity matrix. Thus every 2 × 2 matrix A sa...

If , then show that

where I denotes the 2 × 2 identity matrix. Thus every 2 × 2 matrix A satisfies the equation

A2 − (trace A) A + (det A) I = 0

where det A = ad − bc denotes the determinant of the matrix A, and trace A denotes the sum of its diagonal elements. This result is the 2-dimensional case of the Cayley Hamilton theorem of Section 6.3.

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Solutions For Problems in Chapter 3.4

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