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Verify the statements in Exercises $19-24 .$ The matrices are square.If $A$ is similar to $B,$ then $A^{2}$ is similar to $B^{2}$

$A^{2}$ is similar to $B^{2}$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 4

Eigenvectors and Linear Transformations

Vectors

Oregon State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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Okay, so for a problem, 20 were given the two to similar matrices. So by our definition of similar matrix, that means we There's Derek. Six. There exists on the convertible matrix p such that a few times b times p m burst is a So this is our room assumption. Now we want to show that he squared is similar to be square now, To do that, we first consider a square to be a time saver. Now we substitute this expression of a So we have the PM's be times P embers does be times. He'd have to be times p verse now because matrix multiplication is associative and we can calculate p first times peepers. So we have this and we kept with peace be times beavers then we who have we will have p times b squared times p yours. Now this shows that a squared is similar to

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