# Multiply the following matrices: A=begin{bmatrix} -2 & 1 &51 & 4&-5 end{bmatrix} B=begin{bmatrix}-1 & 7 2 & -23&4 end{bmatrix} AB=?

Multiply the following matrices:
$A=\left[\begin{array}{ccc}-2& 1& 5\\ 1& 4& -5\end{array}\right]B=\left[\begin{array}{cc}-1& 7\\ 2& -2\\ 3& 4\end{array}\right]$ AB=?
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Step 1
The matrix are given :
$A=\left[\begin{array}{ccc}-2& 1& 5\\ 1& 4& -5\end{array}\right]$
$B=\left[\begin{array}{cc}-1& 7\\ 2& -2\\ 3& 4\end{array}\right]$
The product of two matrices are,
$A\cdot B=\left[\begin{array}{ccc}-2& 1& 5\\ 1& 4& -5\end{array}\right]\cdot \left[\begin{array}{cc}-1& 7\\ 2& -2\\ 3& 4\end{array}\right]$
Step 2
Solving the product of matrices,
$A\cdot B=\left[\begin{array}{ccc}-2& 1& 5\\ 1& 4& -5\end{array}\right]\cdot \left[\begin{array}{cc}-1& 7\\ 2& -2\\ 3& 4\end{array}\right]$
$=\left[\begin{array}{cc}\left(-2×1\right)+\left(2×1\right)+\left(5×3\right)& \left(-2×7\right)+\left(1×-2\right)+\left(5×4\right)\\ \left(1×-1\right)+\left(4×2\right)+\left(-5×3\right)& \left(1×7\right)+\left(4×-2\right)+\left(-5×4\right)\end{array}\right]$
$=\left[\begin{array}{cc}2+2+15& -14-2+20\\ -1+8-15& 7-8-20\end{array}\right]$
$=\left[\begin{array}{cc}19& 4\\ -8& -21\end{array}\right]$
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