Prove or disprove that, for matrices A,B,C for which the following
operations are defined:
a. A*(B+C) = A*B + A*C
b. A+(B*C) = (A+B)(A+C)
It's straightforward to create a matrix of some size, and show that these relations are true. However, we should strive to prove them for any size of matrix.
Let's look at what we do with the elements of a matrix when we multiply it with another matrix.
Denote the elements of matrix A by A(row, column) = A(i, j).
i.e. the top left element in the matrix is (1,1). Looking across the top row from left to right we have (1,1),(1,2),(1,3),......
So what happens when we multiply two matrices? It's a sum ...
Equalities are proven/disproven for set operations of matrices.