If A and B have the same trace , determinant , rank , and eigenvalues , then the matrices are similar.
Since the diagonal entries of matrix A are 1 therefore, the trace of the matrix A is 2. Also, the diagonal entries of matrix B are 1 therefore, the trace of the matrix B is also 2.
Determinant of the matrices will be the product of diagonal entries. Therefore, the determinant of both the matrices is 1.
Rank of a matrix is the number of non zero rows. Therefore, the rank of matrix A and matrix B is 2.
The eigen values of a diagonal matrix is the elements in its main diagonal. Therefore, eigen values of matrix
Since, matrices A and B have the same trace, rank, determinant and eigen values therefore the matrices are similar.
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