Suppose that a 2 times 2 matrix B has eigenvalues lambda1 1

Suppose that a 2 times 2 matrix B has eigenvalues lambda_1 = -1 and lambda_2 = 2. Determine the following: (a) the eigenvalues of (B^2 + B - 2I)^-1 (b) the determinant of B^3 - B + 2I (c) the trace of B^2 -2B + 3I

Solution

The eigenvalues of (B²+B-2I)^-1 are 1/((-1)²+(-1)-2), 1/((2)²+(2)-2)

The eigenvalues of (B²+B-2I)^-1 are -1/2 , 1/4