Find the Matrix Product When Possible $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$

question 428

Multiple Choice

Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

• A)
• \(\mathrm{AB}=\left[\begin{array}{crl}
• 0 & 2 & 1 \\
• 0 & -1 & -1 \\
• 0 & 2 & 1
• \end{array}\right] ; \mathrm{BA}=\left[\begin{array}{rrr}
• 0 & 1 & 0 \\
• -1 & 0 & 0 \\
• 2 & -2 & 0
• \end{array}\right]\)
• B)
• \[\mathrm { AB } = \left[ \begin{array} { r r r }
• 0 & - 1 & 0 \\
• 0 & - 1 & 0 \\
• 1 & 0 & 0
• \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r }
• 0 & - 1 & 0 \\
• 0 & - 1 & 0 \\
• 1 & 0 & 0
• \end{array} \right]\]
• C)
• \[\mathrm { AB } = \left[ \begin{array} { r r r }
• 0 & - 1 & 0 \\
• - 1 & 2 & 0 \\
• 2 & - 2 & 0
• \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c }
• 0 & 0 & - 1 \\
• 0 & 1 & 1 \\
• 0 & 0 & - 1
• \end{array} \right]\]
• D)
• \[A B = \left[ \begin{array} { r r r }
• 0 & 1 & 0 \\
• - 1 & 0 & 0 \\
• 2 & - 2 & 0
• \end{array} \right] ; B A = \left[ \begin{array} { c r l }
• 0 & 2 & 1 \\
• 0 & - 1 & - 1 \\
• 0 & 2 & 1
• \end{array} \right]\]

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