# Find if possible the matrices: a. AB b. BA. A=begin{bmatrix}1 & -1&4 4 & -1&32&0&-2 end{bmatrix} , B=begin{bmatrix}1 & 1&0 1 & 2&41&-1&3 end{bmatrix}

Find if possible the matrices:
a. AB b. BA.
$A=\left[\begin{array}{ccc}1& -1& 4\\ 4& -1& 3\\ 2& 0& -2\end{array}\right],B=\left[\begin{array}{ccc}1& 1& 0\\ 1& 2& 4\\ 1& -1& 3\end{array}\right]$
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StrycharzT
Step 1
Matrix:
$A=\left[\begin{array}{ccc}1& -1& 4\\ 4& -1& 3\\ 2& 0& -2\end{array}\right]$
$B=\left[\begin{array}{ccc}1& 1& 0\\ 1& 2& 4\\ 1& -1& 3\end{array}\right]$
Step 2
AB
$=\left[\begin{array}{ccc}1\cdot 1+\left(-1\right)\cdot 1+4\cdot 1& 1\cdot 1+\left(-1\right)\cdot 2+4\cdot \left(-1\right)& 1\cdot 0+\left(-1\right)\cdot 4+4\cdot 3\\ 4\cdot 1+\left(-1\right)\cdot 1+3\cdot 1& 4\cdot 1+\left(-1\right)\cdot 2+3\cdot \left(-1\right)& 4\cdot 0+\left(-1\right)\cdot 4+3\cdot 3\\ 2\cdot 1+0\cdot 1+\left(-2\right)\cdot 1& 2\cdot 1+0\cdot 2+\left(-2\right)\cdot \left(-1\right)& 2\cdot 0+0\cdot 4+\left(-2\right)\cdot 3\end{array}\right]$
$=\left[\begin{array}{ccc}4& -5& 8\\ 6& -1& 5\\ 0& 4& -6\end{array}\right]$
Step 3
$BA=\left[\begin{array}{ccc}5& -2& 7\\ 17& -3& 2\\ 3& 0& -5\end{array}\right]$
Jeffrey Jordon