Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e., b M₂ (R) = { [ a &] | a,b,c,d ER}. Define matrix addition and matrix multiplication in M₂ (R) as follows b₁ + b₂ a₁ b₁ c₁d₁ a2 b₂ 0₂ d₂ = [3 a₁ + a₂ C₁+0₂ 1₁ d₁ + d₂ [a ;] + [ ][ a2 b₂ a₁a₂+ b₁c₂ a1b₂ + b₁d₂ a1 b₁ c₁d₁ 0₂ d₂ = 1. Show that M₂ (R) is a ring under addition and multiplication defined above. [No need to show matrix addition and matrix multiplication are binary operations in M₂(R).] 2. Is the ring M₂ (R) commutative? Justify. 3. Does the ring have a unity? If so, what is it?

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