Question: Two matrices A, B Mn(R) are called similar if B = SAS1 for some invertible matrix S GLn(R). Question 1. Prove the following: Every square

Two matrices A, B Mn(R) are called similar if B = SAS1 for some invertible matrix S GLn(R).

Question 1. Prove the following:

Every square matrix A is similar to itself.

If A is similar to B, then B is similar to A.

If A is similar to B, and B is similar to C, then A is similar to C.

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