Question

If $A = \begin{pmatrix} -1 & -3 \ -1 & 5 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & -2 \ 6 & -3 \end{pmatrix}$, then $AB = \begin{pmatrix} & \\ & \end{pmatrix}$ and $BA = \begin{pmatrix} & \\ & \end{pmatrix}$. Does $AB = BA$ for any two square matrices $A$ and $B$ of the same size? No

          If $A = \begin{pmatrix} -1 & -3 \ -1 & 5 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & -2 \ 6 & -3 \end{pmatrix}$, then

$AB = \begin{pmatrix}  &  \\  &  \end{pmatrix}$

and
$BA = \begin{pmatrix}  &  \\  &  \end{pmatrix}$.

Does $AB = BA$ for any two square matrices $A$ and $B$ of the same size?
No

If A =
< p m a t r i x > and B =
< p m a t r i x >, then

AB =
< p m a t r i x >

and
BA =
< p m a t r i x >.

Does AB = BA for any two square matrices A and B of the same size?
No

Added by Daniel A.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Thomas Emment

05/03/2020

Step 1

Step 1: $AB = \begin{pmatrix} -1 & -3 \\ -1 & 5 \end{pmatrix} \begin{pmatrix} 4 & -2 \\ 6 & -3 \end{pmatrix} = \begin{pmatrix} (-1)(4) + (-3)(6) & (-1)(-2) + (-3)(-3) \\ (-1)(4) + (5)(6) & (-1)(-2) + (5)(-3) \end{pmatrix} = \begin{pmatrix} -22 & 11 \\ 26 & -13 Show more…

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If $A = \begin{pmatrix} -1 & -3 \\ -1 & 5 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & -2 \\ 6 & -3 \end{pmatrix}$, then $AB = \begin{pmatrix} & \\ & \end{pmatrix}$ and $BA = \begin{pmatrix} & \\ & \end{pmatrix}$. Does $AB = BA$ for any two square matrices $A$ and $B$ of the same size? No