# Algebra Problems

## Question

Let Alpha be the set of two by to matrices with real number entries
M = 1 1 0 1 ( this is in position 1,2,3,4 format )
Beta = X is a member of set alpha and is | MX = XM or one is an image of the other
Which of the following elements of Alpha lie in Beta
Set 1 ( 1 1 0 1 ) Set 2 ( 1 1 1 1 ) Set 3 ( 0 0 0 0 ) Set 4 ( 1 1 1 0 ) Set 5 ( 1 0 0 1 ) Set 6 ( 0 1 1 0
Explain it step by step.

Prove that if P, Q is a member of Beta then P + Q is an element of Beta where + means the sum of two matrices

Prove that for any integers a and b that A² + B² never leaves a remainder of three when divided by four.

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