• A matrix is a rectangular array of values consisting of intersecting rows and columns.
• An upper-case variable is used to represent a unique matrix much like a lower-case variable represents a unique value.
• The dimensions of a matrix are stated as the number of rows by the number of columns.

• Only matrices with equal dimensions can be added.
• The addition of matrices is commutative. A + B = B + A
• The addition of matrices is associative. (A + B) + C = A + (B + C)

• Only matrices with equal dimensions can be subtracted.
• Subtraction of matrices is not commutative.

If one looks at subtraction as the addition of a negative, then the equation is commutative.

• Subtraction of matrices is not associative.

If one looks at subtraction as the addition of a negative, then the equation is associative.

• A number that is multiplying the matrix is called a Scalar
• The multiplication of a matrix and a scalar is commutative.
• The multiplication of a matrix and a scalar is associative.
• If dividing by a value, multiply by the value's inverse.