Question

Show that multiplication of matrices is not commutative by determining the product matrices ST and TS. Enter your answer by filling in the boxes.

Answer 1

Answer:

ST= $\left[\begin{array}{ccc}-22&20\\10&-10\\\end{array}\right]$ , TS= $\left[\begin{array}{ccc}-6&-8\\-17&-26&\\\end{array}\right]$

Step-by-step explanation:

ST= $\left[\begin{array}{ccc}3&4\\-1&-2&\\\end{array}\right] \left[\begin{array}{ccc}-2&0\\-4&5\\\end{array}\right]$

by multiplying first row with first column and second column, then second row into first column and second column

ST= $\left[\begin{array}{ccc}-6-16&0+20\\2+8&0+10\\\end{array}\right] =$ $\left[\begin{array}{ccc}-22&20\\10&-10\\\end{array}\right]$

TS= $\left[\begin{array}{ccc}-2&0\\-4&5\\\end{array}\right]\left[\begin{array}{ccc}3&4\\-1&-2&\\\end{array}\right]$ = $\left[\begin{array}{ccc}-6+0&-8+0\\-12-5&-16-10\\\end{array}\right]$= $\left[\begin{array}{ccc}-6&-8\\-17&-26\\\end{array}\right]$

Answer 2

since the product of ST n TS are not equal, there by we can conclude that multiplication of matrices is not commutative.