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Type: Multiple-Choice
Category: Matrices
Level: Grade 12
Standards: HSN-VM.C.9
Author: nsharp1
Created: 5 years ago

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Grade 12 Matrices CCSS: HSN-VM.C.9

Jennie is talking with Liz after their math class. Jennie says, from what she understood from the class, that for matrices

$A$ and

$B$ ,

$AB$ is never equal to

$BA$ . Liz thinks that, although this is true in general, there are certain matrices for which

$AB = BA$ . Who is correct, and why?

Jennie is correct. Since the distributive property does not apply, $AB != BA$ , for all matrices.
Liz is correct. One simply has to take the transpose of the two matrices (the rows become columns of each matrix), and then it is usually true that $AB = BA$ .
Liz is correct. For example, the identity matrix with any square matrix of the same size.
Neither is correct. $AB = BA$ is always true for any matrices A, B.