Matrix A:
\begin{bmatrix} 1 & -2 \\ -2 & 5 \end{bmatrix}
Product of Matrices AB:
\begin{bmatrix} 1 & 2 & -1 \\ 6 & -9 & 3\end{bmatrix}
Find Matrix B?
I am assuming that matrix B is 2x3 matrix but how does one go about finding it ?
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2 
- $\begingroup$ Multiply $A^{-1}$ by $AB$. $\endgroup$user124708– user1247082014-09-28 11:06:22 +00:00Commented Sep 28, 2014 at 11:06
- $\begingroup$ $A^{-1} A B = B$ $\endgroup$user137794– user1377942014-09-28 11:06:24 +00:00Commented Sep 28, 2014 at 11:06
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2 Answers
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Two options:
(1) Write down your matrix $B$ as a matrix of unknowns. Then do the matrix multiplication of $A$ and $B$ and equate it to the known $AB$, giving you a system of equations to solve.
Or
(2) If matrix $A$ is invertible, use its inverse.
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We have that $A^{-1}AB=B$ where $A^{-1}$ is the inverse of the (square) matrix $A$
