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 134

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

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Definitions:

Closing Entries

Journal entries made at the end of an accounting period to transfer temporary accounts’ balances to permanent ones, resetting the temporary accounts for the next period.

Journalized

The process of recording transactions in a company's journal, marking the first step in the accounting process.

End-Of-Period Spreadsheet

A financial statement prepared at the conclusion of an accounting period, summarizing the income, expenses, and adjustments to accounts.

Retained Earnings

Retained earnings are the portion of a company's net income that is kept within the company instead of being paid out to shareholders as dividends, often used for reinvestment in the business or to pay down debt.