1. Find the eigenvalues and corresponding eigenvectors of T: R² → R² where the transformation is given by T(x1, X2) = (2x1 – x2, –X1 + 2x2). 2 Also, find the trace and determinant of the matrix A =,...

Ignore first problem (i)

solve only (ii) and (iii) no problem. Plz, do not copy-paste from other sources. It will be highly appreciated.

Extracted text: 1. Find the eigenvalues and corresponding eigenvectors of T: R² → R² where the transformation is given by T(x1, X2) = (2x1 – x2, –X1 + 2x2). 2 Also, find the trace and determinant of the matrix A =, -1 i. ii. What are the eigenvalues of A? and A-1 ? iii. Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P-1AP.