# Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. A=begin{bmatrix}3 & -2 1 & 5end{bmatrix} , B=begin{bmatrix}0 & 0 5 & -6 end{bmatrix}

Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
$A=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$
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Malena
Step 1
Given: $A={\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]}_{2×2},B={\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]}_{2×2}$
Step 2 $AB=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$
$=\left[\begin{array}{cc}3×0-2×5& 3×0+2×6\\ 1×0+5×5& 1×0-6×5\end{array}\right]$
$=\left[\begin{array}{cc}0-10& 0+12\\ 0+25& 0-30\end{array}\right]=\left[\begin{array}{cc}-10& 12\\ 25& -30\end{array}\right]$
$BA=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]=\left[\begin{array}{cc}0×3+0×1& 0×\left(-2\right)+0×5\\ 5×3-6×1& 5×\left(-1\right)-6×5\end{array}\right]$
$=\left[\begin{array}{cc}0+1& 0\\ 15-6& -10-30\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 9& -40\end{array}\right]$
Jeffrey Jordon