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The stochastic group Σ(2, ℝ) consists of all those matrices in GL(2, ℝ) whose column sums...

The stochastic group Σ(2, ℝ) consists of all those matrices in GL(2, ℝ) whose column sums are 1; that is, Σ(2, ℝ) consists of all the nonsingular matrices

[a c]

[b d] with a + b = 1 = c + d

Prove that the product of two stochastic matrices is again stochastic, and that the inverse of a stochastic matrix is stochastic. [abstract algebra] NOTE: the [a c] and [b d] is supposed to be a 2x2 matrix with a c in row 1 and b d in row 2.

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