How to do matrix multiplication - Casio FX-115ES Scientific Calculator

This post is rather exhaustive as regards the matrix capabilities of the calculator. So if the post recalls things you already know, please skip them. Matrix multiplication is at the end.

Let me explain how to create matrices. (If you know how to do it, skip to the operations on matrices, at the end.)

First you must set Matrix calculation
[MODE][6:Matrix]. Then By entering one of the numbers [1:MatA] or [2:Matb] or [3:MatC] you get to choose the dimensions of the matrix
(mxn]. Once finished entering the matrix you clear the screen.
The operations on matrices are available by pressing [Shift][Matrix]
[1:Dim] to change the dimension of a matrix (in fact redefining the matrix)
[2:Data] enter values in a matrix
[3:MatA] access Matrix A
[4:Matb] access Matrix B
[5:MatC] access matrix C
[6:MatAns] access the Answer Matrix (the last matrix calculated)
[7:det] Calculate the determinant of a matrix already defined
[8:Trn] The transpose of a matrix already defined

To add matrices MatA+MatB (MUST have identical dimensions same m and same n, m and n do not have to be the same)
To subtract MatA-MatB. (MUST have identical dimensions, see above)
To multiply MatAxMatB (See below for conditions on dimensions)
To raise a matrix to a power 2 [x2], cube [x3]
To obtain inverse of a SQUARE MatA already defined MatA[x-1]. The key [x-1] is the x to the power -1 key. If the determinant of a matrix is zero, the matrix is singular and its inverse does not exit.

Dimensions of matrices involved in operations must match. Here is a short summary

The multiplication of structured mathematical entities (vectors, complex numbers, matrices, etc.) is different from the multiplication of unstructured (scalar) mathematical entities (regular numbers). As you well know matrix multiplication is not commutative> This has to do with the dimensions.

An mXn matrix has m rows and n columns. To perform multiplication of an kXl matrix by an mXn matrix you multiply each element in one row of the first matrix by a specific element in a column of the second matrix. This imposes a condition, namely that the number of columns of the first matrix be equal to the number of rows of the second.
Thus, to be able to multiply a kXl matrix by am mXn matrix, the number of columns of the first (l) must be equal to the number of rows of the second (m).

So MatA(kXl) * MatB(mXn) is possible only if l=m
MatA(kX3) * Mat(3Xn) is possible and meaningful, but
Mat(kX3) * Mat(nX3) may not be possible.

To get back to your calculation, make sure that the number of columns of the first matrix is equal to the number of rows of the second. If this condition is not satisfied, the calculator returns a dimension error. The order of the matrices in the multiplication is, shall we say, vital.