Name: Matrix Multiplication and Associated Properties
Uploaded: 2019-07-19
Duration: 6 min 22 s
Description: We learned the addition and subtraction of matrices. Is it possible to multiply the two matrices? Watch this video and learn to multiply two matrices together.

Question

If

A = [\begin{matrix} 1 \\ - 4 \\ 3 \end{matrix}]

and

B = [\begin{matrix} - 1 & 2 & 1 \end{matrix}]

, verify that

(AB)' = B' A'

.

Accepted Answer

Given,

$A = [\begin{matrix} 1 \\ - 4 \\ 3 \end{matrix}]$ and $B = [\begin{matrix} - 1 & 2 & 1 \end{matrix}]$

To proof : $(AB)' = B' A'$

Now,

$AB = [\begin{matrix} 1 \\ - 4 \\ 3 \end{matrix}] [\begin{matrix} - 1 & 2 & 1 \end{matrix}]$

$AB = [\begin{matrix} 1 \times (- 1) & 1 \times 2 & 1 \times 1 \\ (- 4) \times (- 1) & (- 4) \times 2 & (- 4) \times 1 \\ 3 \times (- 1) & 3 \times 2 & 3 \times 1 \end{matrix}]$

$AB = [\begin{matrix} - 1 & 2 & 1 \\ 4 & - 8 & - 4 \\ - 3 & 6 & 3 \end{matrix}]$

$(AB)' = [\begin{matrix} - 1 & 4 & - 3 \\ 2 & - 8 & 6 \\ 1 & - 4 & 3 \end{matrix}] . . . . . . . . . . (1)$

Taking,

$B' A' = [\begin{matrix} - 1 \\ 2 \\ 1 \end{matrix}] [\begin{matrix} 1 & - 4 & 3 \end{matrix}]$

$B' A' = [\begin{matrix} (- 1) \times 1 & - 1 \times (- 4) & (- 1) \times 3 \\ 2 \times 1 & 2 \times (- 4) & 2 \times 3 \\ 1 \times 1 & 1 \times (- 4) & 1 \times 3 \end{matrix}]$

$B' A' = [\begin{matrix} - 1 & 4 & - 3 \\ 2 & - 8 & 6 \\ 1 & - 4 & 3 \end{matrix}]$ $. . . . . . . . . (2)$

From equation $(1)$ and $(2)$ , we get

$(AB)' = B' A'$ .

If $A = [\begin{matrix} 1 \\ - 4 \\ 3 \end{matrix}]$ and $B = [\begin{matrix} - 1 & 2 & 1 \end{matrix}]$ , verify that $(AB)' = B' A'$ .

Important Questions on Matrices

Learn and Prepare for any exam you want !

If A=1-43 and B=-121, verify that AB'=B'A'.

Important Questions on Matrices

Learn and Prepare for any exam you want !

If $A = [\begin{matrix} 1 \\ - 4 \\ 3 \end{matrix}]$ and $B = [\begin{matrix} - 1 & 2 & 1 \end{matrix}]$ , verify that $(AB)' = B' A'$ .