Question

Consider the matrices.


Show that multiplication of matrices is not commutative by determining the product matrices ST and TS.


Help, please?

Answer 1

Supposing two matrices, S and T, the product ST is different than TS, that is, they result in different matrices, thus, they are not commutative.

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The matrices are:

$T = \left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]$

$S = \left[\begin{array}{cc}5&6\\7&8\\\end{array}\right]$

When two matrices are multiplied, the lines of the first are multiplied by the columns of the second.

The product ST is:

$ST = \left[\begin{array}{cc}1&2\\3&4\\\end{array}\right] \times \left[\begin{array}{cc}5&6\\7&8\\\end{array}\right] = \left[\begin{array}{cc}1(5)+2(7)&1(6)+2(8)\\3(5)+4(7)&3(6)+4(8)\\\end{array}\right] = \left[\begin{array}{cc}19&22\\43&50\\\end{array}\right]$

The product TS is:

$TS = \left[\begin{array}{cc}5&6\\7&8\\\end{array}\right] \times \left[\begin{array}{cc}1&2\\3&4\\\end{array}\right] = \left[\begin{array}{cc}5(1)+6(3)&5(2)+6(4)\\7(1)+8(3)&7(2)+8(4)\\\end{array}\right] = \left[\begin{array}{cc}23&34\\31&44\\\end{array}\right]$

Different matrices, thus, the product of matrices is not commutative.

A similar problem is given at https://brainly.com/question/20683823