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→Multiplication of matrices: expand
Matrix multiplication is [[associativity|associative]]. However, matrix multiplication is ''not'' [[commutativity|commutative]]. That is, it is possible for <math>AB \neq BA</math>.
Matrix multiplication is [[associativity|associative]]. However, matrix multiplication is ''not'' [[commutativity|commutative]]. That is, it is possible for <math>AB \neq BA</math>.
The <math>n \times n</math> [[identity matrix]] <math>I_n</math> satisfies the property:
<center><math>AI_n = I_n A = A</math></center>
for all <math>n \times n</math> matrices <math>A</math>.
Moreover, every square matrix <math>A</math> with nonzero [[determinant]] has an inverse matrix <math>B</math> such that
<center><math>AB = BA = I_n</math></center>
This means that for every positive integer <math>n</math>, the set of all <math>n \times n</math> matrices with nonzero determinant form a [[group]] under matrix multiplication. This group is known as the [[general linear group]] <math>GL_{n}(\mathbb{R})</math>.
===Matrix concepts===
===Matrix concepts===