(a) The general linear group GL (R) is the set of 2 2 matrices [a...

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(a) The general linear group GL₂ (R) is the set of 2 × 2 matrices [a b], where a, b, c, d are real numbers such that ad - bc #0. Prove that GL₂ (R) is a group under matrix multiplication, which is defined by a C b d X e h = ae+bg af+bh ce + dg cf +dh (a) The general linear group GL₂ (R) is the set of 2 × 2 matrices [a b], where a, b, c, d are real numbers such that ad - bc #0. Prove that GL₂ (R) is a group under matrix multiplication, which is defined by a C b d X e h = ae+bg af+bh ce + dg cf +dh