Find \( A B \), if possible. \[ A=\left[\begin{array}{rrr}5 & -1 & 8 \\ 0 & 4 & -5\end{array}\right] \quad B=\left[\begin{array}{rr}-7 & 2 \\ 9 & 3\end{array}\right] \]
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Beyond the Answer
To find the product \( AB \), we first need to confirm whether the multiplication is possible. The number of columns in matrix \( A \) must be equal to the number of rows in matrix \( B \). Matrix \( A \) is a \( 2 \times 3 \) matrix (2 rows and 3 columns), and matrix \( B \) is a \( 2 \times 2 \) matrix (2 rows and 2 columns). Since the number of columns in \( A \) (3) does not equal the number of rows in \( B \) (2), the product \( AB \) is not possible. Therefore, we cannot calculate \( AB \) as the matrices are incompatible for multiplication.
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