Matrix subtraction is finding the resultant matrix by subtraction corresponding elements of two or more matrices. While finding the difference of two matrices, the order of matrices should be same, meaning that they should have same dimensions.

It means 2x2 matrix can be subtracted from another 2x2 matrix. The two matrix should have same number of rows and columns, or else its not possible

There is only one rule for matrix subtraction.

The matrices should have same dimensions (number of rows and columns).

Having a different dimension will not allow you to subtract the matrices.

For example, if there are two matrices A and B

A = [89 45 21] and B = [23 33 34]

The matrices A and B have same dimensions (1x3), so subtraction is possible. The resultant matrix will be

A - B = [89-23 45-33 21-34] = [66 12 -13]

Write down the matrices to be subtracted

There can be any number of matrices to be subtracted, as long as they have same dimensions

Subtract the corresponding elements of the matrices

And The resultant matrix ader subtraction will also have the same dimensions as the matrices being subtracted

For example there are two matrices X and Y

D = [d1 d2 d3] and E = [e1 e2 e3]

Then, D - E = [d1-e1 d2-e2 d3-e3]

Its not possible to subtract two matrices with differrent number of rows and columns

Matrix subtraction is not commutative.

The order in which the matrices are subtracted matters.

If there are two matrices J and K

J = [21 22 23] and K = [45 34 56]

Then, J - K = [21-45 22-34 23-56] = [-24 -12 -33]

And K - J = [45-21 34-22 56-23] = [24 12 33]

Therefore, J - K is not equal to K - J

Matrix subtraction is associative.

If there are three matrices P, Q and R

Here, P - (Q - R) = (P - Q) - R

Therefore, matrix subtraction is associative

Here are two matrices subtraction of dimensions 1x3

R = [90 21 233] and S = [45 75 98]

R - S = [90-45 21-75 233-98] = [45 -54 135]

There fore, R - S = [45 -54 135]

Here are two matrices subtraction of dimensions 1x3

T = [34 56 78] and U = [23 45 67]

T - U = [34-23 56-45 78-67] = [11 11 11]

There fore, T - U = [11 11 11]

Here are two matrices subtraction of dimensions 1 x 4

V = [53 55 67 99] and W = [23 45 67 89]

V - W = [53-23 55-45 67-67 99-89] = [30 10 0 10]

There fore, V - W = [30 10 0 10]

Here the 3rd element is 0, it must be written as 0, as it is a valid result

Here are two matrices subtraction of dimensions 1 x 6

R = [45 65 234 46 1/2 -56] and S = [23 76 67 89 1/2 34]

R - S = [45-23 65-76 234-67 46-89 1/2-1/2 -56-34] = [22 -11 167 -43 0 -90]

There fore, R - S = [22 -11 167 -43 0 -90]

The two matrices, F and G are given as

F = [-23 -45 -65 ] and G = [-45 -67 -89]

F - G = [-23+45 -45+67 -65+89]

F - G = [22 22 24]

Therefore, F - G = [22 22 24]