Prove that if A and B are similar then IA B Is the converse

Last updated: 6/29/2023

Prove that if A and B are similar then IA B Is the converse true Illustrate the results using the matrices 200 0 1 2 030 HECH P 1 12 p 1 1 4 2 2 2 5 A P AP 11 where B P 1AP STEP 1 First note that A and B are similar B 11 200 BBB 030 001 333 1 4 2 1 1 0 0 2 1 1 1 0 2 3 5 10 4 2 STEP 3 Does B A 8 6 4 4 10 7 000 000 STEP 2 Take the determinant of B by expanding along the first row B 3 5 16 10 012 1 1 2 2 25 8 101 4 7 10 1 1 0 0 2 1 8