Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e.,a bM₂ (R) = {[%• { [ @ $ ] 1a,b,c,dER}.dDefine matrix addition and matrix multiplication in M₂ (R) as followsa1 b₁d₁a₁ + a₂ b₁ + b₂;] + [=az b₂0₂ d₂[C1a11][² :]a2 b₂d₂a₁a2+ b₁c₂ a1b₂ + b₁d₂c₁a₂+d₂c₂ c₁b₂+d₁d₂:].c₁d₁1. 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?

The given matrix is M2ℝ=abcd: a,b,c,d∈ℝ To find : (a) M2ℝ is a ring under addition and…

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?