Let R be the ring of all 2 x 2 real matrices. A. Assume that A...

Let R be the ring of all 2 x 2 real matrices.

A. Assume that A is an element of R such that AB=BA for all B elements of R. Prove that A is a scalar multiple of the identity matrix.

B. Prove that {0} and R are the only two ideals.

Hint: Use the Matrices E11, E12, E21, E22.

Expert Solution

milcah answered 3 years ago

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