## An introduction to sets, groups, and matrices |

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a o b A U B a(bc AABC ab)c adjugate matrix algebra of sets anti-clockwise rotation associative law B O C B U C binary operation brand brand X cofactor corresponding elements defined Defn determinant drank equations EXERCISES 1.3 following sets group G Hence idempotent identity element inverse inverse matrix Law 10b Law 3a Let x e m x n matrix mathematicians who speak matrix addition matrix given matrix multiplication matrix of order non-singular matrix null matrix null set number of columns number of elements number of rows operation of addition operation of matrix operation of multiplication ordinary algebra positive integers prime number proper subset real numbers region marked region shaded rotation in space rotation M acting scalar set of elements Show Simplify singular matrix skew-symmetric matrix subtraction symbol symmetric matrix Transpose unit element unit matrix universal set Venn-Euler diagram Verify worn