# Matrices A and B are defined as follows, Find the product: BA A=begin{bmatrix}1 & 2 & 3 end{bmatrix} B= begin{bmatrix}4 5 6 end{bmatrix}

Matrices A and B are defined as follows, Find the product: BA $A=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]B=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$
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Step 1
Accoding to the question, we have to find the poduct BA, where the matrices A and B are respectively.
In addition to multiplying a matrix by a scalar, we can multiply two matrices. Finding the product of two matrices is only possible when the inner dimensions are the same, meaning that the number of columns of the first matrix is equal to the number of rows of the second matrix.
As in the number of row of matrix B is 3 and the number of collum of matrix A is 3 and also it fulfil the condition of product BA.
Step 2
Rewrite the given matrices $A=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]B=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$ now for the product of BA, proceed as follows, $BA=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$
$=\left[\begin{array}{ccc}4\cdot 1& 4\cdot 2& 4\cdot 3\\ 5\cdot 1& 5\cdot 2& 5\cdot 3\\ 6\cdot 1& 6\cdot 2& 6\cdot 3\end{array}\right]$
$=\left[\begin{array}{ccc}4& 8& 12\\ 5& 10& 15\\ 6& 12& 18\end{array}\right]$ So, the product $BA=\left[\begin{array}{ccc}4& 8& 12\\ 5& 10& 15\\ 6& 12& 18\end{array}\right]$
Hence, the product $BA=\left[\begin{array}{ccc}4& 8& 12\\ 5& 10& 15\\ 6& 12& 18\end{array}\right]$
Jeffrey Jordon