Multiplying 2×2 matrix

Multiplying 2×2 matrix can be a tedious, time-consuming and error-prone task. Therefore, we have prepared for you a calculator capable of solving this operation instantly and for that, you just have to fill in the values of the 2x2 matrix you want to multiply.

With this tool you will also be able to calculate the square of a 2×2 matrix. In this case, the values of the elements must match each other. When you have it ready, click the calculate button and you will know how the matrix have been multiplied step by step and the final result. 

Conditions for multiplying matrix

Multiplying 2x2 matrix

There is only one condition that dictates whether two matrix can multiply each other and that is that the number of columns of A must be equal to the number of rows of matrix B. The result of multiplying both matrix will be a matrix with the number of columns of A and the number of rows of B.

A mxn x B nxp = C mxp

If we meet this requirement, we can multiply matrix as follows.

How to multiply matrix

To multiply matrix we must add the product obtained by multiplying each element of row i of matrix A by each element of column j of matrix B. The result will be the element cij of the product matrix.

In other words, we have to multiply rows of the matrix A by the columns of the matrix B. The following practical example shows this more clearly how to multiply 3×3 matrix:

Multiplying 3x3 matrices

In our case, as we are talking about 2×2 matrix, the process is greatly simplified.

Multiplying 2×2 matrix in Excel

If you want to make your own matrix multiplication calculatorIf you do not have a matrix, you can use Excel to make one in a matter of seconds. This is very useful since we can make a spreadsheet to multiply fractions of different sizes but always respecting the rule that the number of columns of the first matrix is the same as the number of rows of the second matrix.

As we are working with 2×2 matrixIf we want to display the result, we simply write the values of each element of the matrix in an empty cell of the spreadsheet and when it is done, we select a range of empty cells in which we want the result to appear.

The next step is to write a Excel formula that will allow us to multiply the arrays. This formula will show the range of cells that correspond to the matrix A and the same for matrix B. In such a way that we will have something like this:

=MMULT(A1:B2;D1:E2)

When the formula is written, you must press CTRL + Shift keys (shift) on your keyboard and without releasing the ENTER key. In this way, Excel will display the result as a matrix multiplication. If you do not do this, only one element of the operation will appear but the rest will not.

If you have any questions about how to multiply matrix in ExcelLeave us a comment and we will try to help you as soon as possible.

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