Question

Consider the matrices

Answer 1

Explanation:

S =
`\left[\begin{array}{cc}4&1\\-1&-2\end{array}\right]`

T =
`\left[\begin{array}{cc}-5&0\\-4&3\end{array}\right]`

ST =
`\left[\begin{array}{cc}4&1\\-1&-2\end{array}\right]` ×
`\left[\begin{array}{cc}-5&0\\-4&3\end{array}\right]` =
`\left[\begin{array}{cc}14(-5)+1(-4)&(4)0+1(3)\\(-1)(-5)+(-2)(-4)&(-1)0+(-2)(3)\end{array}\right]` =

=
`\left[\begin{array}{cc}-24&3\\13&-6\end{array}\right]`

TS =
`\left[\begin{array}{cc}-5&0\\-4&3\end{array}\right]` ×
`\left[\begin{array}{cc}4&1\\-1&-2\end{array}\right]` =
`\left[\begin{array}{cc}(-5)(4)+(0)(-1)&(-5)(1)+(0)(-2)\\(-4)(4)+3(-1)&(-4)(1)+(3)(-2)\end{array}\right]` =

=
`\left[\begin{array}{cc}-20&-5\\-19&-10\end{array}\right]`

ST ≠ TS