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# How can I divide the two matrices together ?

Last updated date: 22nd Jun 2024
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Hint: First of all , we need to know that the matrix is a rectangular arrangement of elements ( numbers ) into the rows and columns.Technically , the matrices cannot be divided . But if you remember the basic concept of division of two fractions , then one fraction remains the same but the other fraction gets inverted and multiplied to the former fraction for performing the division . In the similar way , if we have to divide two matrices together we must take the inverse of one matrix and multiply it with the other matrix .

Note:The division of two matrices is an undefined function instead we solve $\left[ A \right]{\text{ }} \times {\text{ }}{\left[ B \right]^{ - 1}}$ .Always remember that $\left[ A \right]{\text{ }} \times {\text{ }}{\left[ B \right]^{ - 1}}$ may have a different answer than calculating for ${\text{ }}{\left[ B \right]^{ - 1}} \times \left[ A \right]{\text{ }}$. These are two different problems that can have different solutions .
The number of rows and columns are the same for the original matrix $\;\left[ B \right]$ as that of inverse of that same matrix $\;{\left[ B \right]^{ - 1}}\;$.If the determinant of the matrix comes out to be 0 then the inverse of the matrix does not exist.If we multiply the inverse by the original matrix then their product will be equal to the identity matrix always .