Let \( A=\left[\begin{array}{cc}-5 & 0 \\ 0 & 4\end{array}\right] \) and \( B=\left[\begin{array}{cc}-2 & 0 \\ 0 & 1\end{array}\right] \). Find each matrix below. If a matrix is not defined, click on "Undefined". (a) \( B A= \) \( \square \) (b) \( A B= \) \( \square \) (c) \( B^{2}- \) \( \square \) Check

To calculate \(B A\) and \(A B\), we will perform matrix multiplication. (a) \(B A = \left[\begin{array}{cc}-2 & 0 \\ 0 & 1\end{array}\right] \left[\begin{array}{cc}-5 & 0 \\ 0 & 4\end{array}\right] = \left[\begin{array}{cc}(-2)(-5) + (0)(0) & (-2)(0) + (0)(4) \\ (0)(-5) + (1)(0) & (0)(0) + (1)(4)\end{array}\right] = \left[\begin{array}{cc}10 & 0 \\ 0 & 4\end{array}\right]\) (b) \(A B = \left[\begin{array}{cc}-5 & 0 \\ 0 & 4\end{array}\right] \left[\begin{array}{cc}-2 & 0 \\ 0 & 1\end{array}\right] = \left[\begin{array}{cc}(-5)(-2) + (0)(0) & (-5)(0) + (0)(1) \\ (0)(-2) + (4)(0) & (0)(0) + (4)(1)\end{array}\right] = \left[\begin{array}{cc}10 & 0 \\ 0 & 4\end{array}\right]\) (c) \(B^{2} = B \times B = \left[\begin{array}{cc}-2 & 0 \\ 0 & 1\end{array}\right] \left[\begin{array}{cc}-2 & 0 \\ 0 & 1\end{array}\right] = \left[\begin{array}{cc}4 & 0 \\ 0 & 1\end{array}\right]\) So the results are: (a) \( B A = \left[\begin{array}{cc}10 & 0 \\ 0 & 4\end{array}\right] \) (b) \( A B = \left[\begin{array}{cc}10 & 0 \\ 0 & 4\end{array}\right] \) (c) \( B^{2} = \left[\begin{array}{cc}4 & 0 \\ 0 & 1\end{array}\right] \)