how matrix multiplication is possible matrix division is also possible or not?

Answer 1

While there may not technically be such a thing as matrix division, an idea of it can be easily extrapolated from elementary mathematics. We know that division by a number undoes multiplication by that number. We might define matrix division as a process to do the same. Let x and y each be any number.

xy = z

Simple algebra tells us that dividing both sides by y yields a true statement for the same variables:

x = z / y

Which is the same as

x=z*(1/y)


Or, x equals z times the inverse of y. There are multiple ways to take the inverse of a matrix. So matrix division can be defined as multiplying both sides of an equation by the inverse of a matrix. There is one difference between elementary division and matrix division, however. Because matrix multiplication is not commutative, when multiplying both sides of an equation by the inverse of a matrix, it is important to put that inverted matrix in the proper location. For two by two matrices this should be as follows:

AB = C becomes B = (A − 1)C

and

AB = C becomes A = C(B − 1)

Answer 2

There is not in general matrix division, only if the matrix in question has an inverse. Division is only possible where the number being divided by has an inverse. This is why you cannot divide by 0, in the field of the real numbers (if you know what "field" means), 0 has no multiplicative inverse, so you cannot divide by it. Multiplication by 0 is defined but not division - similarly, multiplication is defined on all square matrices, but division only for those with inverses (that is, B is the inverse of A if AB = BA = I, the identity matrix)

Answer 3

A divided by B is defined as A multiplied by the multiplicative inverse of B.

However, not all non-zero matrices have multiplicative inverses.

Hence, the quotient of two non-zero matrices is not always defined.

Hence, it isn't worth the trouble to use the language and notation of division.

Answer 4

matrix division is simply multiplying by the inverse,
but 'matrix division' is technically not possible

Answer 5

No,it is no possible