whats the formula to solve

• A=[12 4] 

      [10 -2]
 B=[3 -5]
     [6 -7] FORMULA ND HOW TO SOLVE A.B



 

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{are} \mathrm{not} \mathrm{able} \mathrm{to} \mathrm{understand} \mathrm{your} \mathrm{problem}. \mathrm{There} \mathrm{are} \mathrm{no} \mathrm{equations}, \mathrm{hence} \\ \mathrm{there} \mathrm{is} \mathrm{nothing} \mathrm{to} \mathrm{solve}. \\ \mathrm{We} \mathrm{guess} \mathrm{you} \mathrm{might} \mathrm{be} \mathrm{looking} \mathrm{for} \mathrm{product} \mathrm{of} \mathrm{two} \mathrm{given} \mathrm{matrices} \\ \mathrm{A}=\left[\begin{array}{cc}12& 4\\ 10& -2\end{array}\right] \\ \mathrm{B}=\left[\begin{array}{cc}3& -5\\ 6& -7\end{array}\right] \\ \mathrm{When} \mathrm{we} \mathrm{multiply} \mathrm{two} \mathrm{square} \mathrm{matrix} \mathrm{of} \mathrm{same} \mathrm{order} \mathrm{then} \mathrm{resultant} \mathrm{matrix} \mathrm{is} \\ \mathrm{also} \mathrm{of} \mathrm{same} \mathrm{order}. \\ \mathrm{AB} \\ =\left[\begin{array}{cc}12& 4\\ 10& -2\end{array}\right] \left[\begin{array}{cc}3& -5\\ 6& -7\end{array}\right] \\ =\left[\begin{array}{cc}12\times 3+4\times 6& 12\times \left(-5\right)+4\times \left(-7\right)\\ 10\times 3+\left(-2\right)\times 6& 10\times \left(-5\right)+\left(-2\right)\times \left(-7\right)\end{array}\right] \\ =\left[\begin{array}{cc}36+24& -60-28\\ 30-12& -50+14\end{array}\right] \\ =\left[\begin{array}{cc}60& -88\\ 18& -36\end{array}\right] \\ \mathbf{\Rightarrow }\mathbf{AB}\mathbf{=}\left[\begin{array}{cc}\mathbf{60}& \mathbf{-}\mathbf{88}\\ \mathbf{18}& \mathbf{-}\mathbf{36}\end{array}\right] \end{gathered}$$

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