Problems 28 through 30 develop a method of computing powers of a square matrix.

If

then show that

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

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.

A= b C d = [a