Let $A=\left[\begin{array}{ccc}0 & -3 & 2 \\ 7 & 1 & 9\end{array}\right]$ and $B=\left[\begin{array}{cc}-10 & 3 \\ 5 & 0 \\ 8 & -7\end{array}\right]$ Find $A B$, if possible. Entry in first row, first column is [Choose ] Entry in first row, second column is [Choose] Entry in second row, first column is [Choose] Entry in second row, second column is [Choose]

Step 1 ：Let \(A=\left[\begin{array}{ccc}0 & -3 & 2 \ 7 & 1 & 9\end{array}\right]\) and \(B=\left[\begin{array}{cc}-10 & 3 \ 5 & 0 \ 8 & -7\end{array}\right]\)

Step 2 ：We need to find the product of matrices A and B, denoted as \(AB\)

Step 3 ：The entry in the first row and first column of the resulting matrix is calculated as \(0*(-10) + (-3)*5 + 2*8 = 1\)

Step 4 ：The entry in the first row and second column of the resulting matrix is calculated as \(0*3 + (-3)*0 + 2*(-7) = -14\)

Step 5 ：The entry in the second row and first column of the resulting matrix is calculated as \(7*(-10) + 1*5 + 9*8 = 7\)

Step 6 ：The entry in the second row and second column of the resulting matrix is calculated as \(7*3 + 1*0 + 9*(-7) = -42\)

Step 7 ：So, the product of matrices A and B is \(\boxed{\left[\begin{array}{cc}1 & -14 \ 7 & -42\end{array}\right]}\)