Question Find the product of the following two matrices. \[ \left[\begin{array}{ccc}0 & -4 & -4 \\ -5 & 0 & 4\end{array}\right]\left[\begin{array}{cc}0 & -1 \\ 2 & 0 \\ -2 & 1\end{array}\right] \]

To find the product of two matrices, we need to follow the rules of matrix multiplication. Given matrices: \[ A = \left[\begin{array}{ccc}0 & -4 & -4 \\ -5 & 0 & 4\end{array}\right] \] \[ B = \left[\begin{array}{cc}0 & -1 \\ 2 & 0 \\ -2 & 1\end{array}\right] \] The product of matrices A and B is denoted as AB. To find the product AB, we need to perform the following steps: 1. Multiply the rows of matrix A with the columns of matrix B. 2. The resulting product will be a matrix with the same number of rows as matrix A and the same number of columns as matrix B. Let's calculate the product AB step by step. Matrices by following steps: - step0: Solution: \(\left[\begin{array}{lll}{0}&{-4}&{-4}\\{-5}&{0}&{4}\end{array}\right]\times \left[\begin{array}{ll}{0}&{-1}\\{2}&{0}\\{-2}&{1}\end{array}\right]\) - step1: Multiply the terms: \(\left[\begin{array}{ll}{0\times 0-4\times 2-4\left(-2\right)}&{0\times \left(-1\right)-4\times 0-4\times 1}\\{-5\times 0+0\times 2+4\left(-2\right)}&{-5\left(-1\right)+0\times 0+4\times 1}\end{array}\right]\) - step2: Evaluate: \(\left[\begin{array}{ll}{0}&{-4}\\{-8}&{9}\end{array}\right]\) The product of the two matrices is: \[ AB = \left[\begin{array}{ll}0 & -4 \\ -8 & 9\end{array}\right] \]