Prove that if A and B are similar, then |A| = |B|. Is the converse true? Illustrate the results using the matrices -2 0

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Prove That If A And B Are Similar Then A B Is The Converse True Illustrate The Results Using The Matrices 2 0 1 (53.81 KiB) Viewed 42 times

Prove that if A and B are similar, then |A| = |B|. Is the converse true? Illustrate the results using the matrices -2 0 0 * - [*] -- [ A = 03 0 B = 0 0 1 P-¹AP = where B = P-¹AP. STEP 1: First note that A and B are similar. -2 0 0 03 0 0 0 1 |B| = 3 = = 1 -1 0 1 4-2 0-2 1 O No 1 -1 0 1 4-2 3 -5 -10 -8 6 10 4-4 -7 0-2 1 1-₁ [ P = STEP 3: Does |B| = |A|? Yes HEEE +5(16) 10( 0 1 2 -1 1 2 STEP 2: Take the determinant of B by expanding along the first row. - -2 25 0 1 2 -1 1 2 -2 2 5 +5 7 p-1 = -8 10 4 -7 - 10 ← → 1 -1 0 1 4-2 0-2 1 "