Let A- 1 -2 3- 3 2 -1 - and B- 2 3- -1 2- 4 -5 - Find AB and BA and show that AB- BA-

AB=[ 1 amp; 2 amp; 3; 3 amp; 2 amp; 1 ][ 2 amp; 3; 1 amp; 2; 4 amp; 5 ] =[ 16 amp; 16; 0 amp; 18 ] ...

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Multiplication of Matrices

Let A=[ 1 -...

Question

Let $A = [\begin{matrix} 1 & - 2 & 3 3 & 2 & - 1 \end{matrix}]$ and $B = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 - 1 & 2 4 & - 5 \end{matrix} ⎤ ⎥ ⎦$ . Find AB and BA and show that $A B \neq B A .$

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A = [\begin{matrix} 1 & - 2 & 3 - 4 & 2 & 5 \end{matrix}]

B = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 4 & 5 2 & 1 \end{matrix} ⎤ ⎥ ⎦

A B

A B \neq B A

a = \frac{- 1}{7}

b = \frac{3}{7},

a b = b a .

A = [\begin{matrix} 4 & 1 3 & 2 \end{matrix}]

B = [\begin{matrix} 1 & 3 4 & 2 \end{matrix}]

A B \neq B A

a > b

a^{b} b^{b} > a^{b} b^{a}

log \frac{b}{a} < log \frac{1 + b}{1 + a}

A = [\begin{matrix} a & b b & a \end{matrix}]

B = [\begin{matrix} p & q r & s \end{matrix}]

b = 0

A B = B A

b \neq 0

A B = B A

\Leftrightarrow

p = s a n d q = r

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