Matrix Multiplication Rules
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Last updated 9:15 AM on 9/18/26
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23 Terms
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Order
The arrangement of a matrix
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What is the order of a matrix
n x m
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What does n mean in orders of matrices
Number of rows
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What does m mean in orders of matrices
Number of columns
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Square matrix
Has the same number of rows as columns
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Identity matrix
When multiplied by another matrix, the matrix will remain unchanged
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Zero matrix
When multiplied by another matrix, that matrix becomes 0
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Is the identity matrix a square matrix?
Yes
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I1
1x1 identity matrix
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I2
2x2 identity matrix
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I3
3x3 identity matrix
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When can you add two matrices
If they have the same order
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Scalar
Number that multiplies a matrix
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What types of matrices can be squared
Square matrices
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Non-conformable
Not possible
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When is matrix multiplication conformable
When the number of columns in matrix A = the number of rows in matrix B
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Attributes of matrix multiplication
-Must be conformable
-Not commutative
-Associative
-Distributive
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How to work out the order of a matrix after multiplication
For matrices (nxm) x (mxq) the order will be (nxq)
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Commutative
a x b = b x a
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What does it mean that matrices are not commutative
a x b does not equal b x a
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When is matrix multiplication commutative
A matrix is squared, a matrix is transformed by the zero or identity matrix
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Distributive
P(Q+R) = PQ + PR
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Associative
(PQ)R = P(QR)