The trace of a 2 × 2 matrix

is defined to be tr(A) = a + d.

(a) Work out the trace of

(b) Prove that if A and B are any 2 × 2 matrices, then tr(αA + bB) = a tr(A) + b tr(B) for any numbers a and b.
(c) Decide whether following results are true or false for general 2 × 2 matrices. If the result is true, prove it, and if the result is false, provide a counter-example.

(i) tr(A⁻¹) = (tr(A))⁻¹
(ii) tr(AB) = tr(BA)

Transcribed Image Text:

A d 4 2 -5