Another problem is, what conditions should be satisfied for multiplication of two matrices

Another problem is, what conditions should be satisfied for multiplication of two matrices

If a matrix A is of order m * N and B is of order p * q, AB can be multiplied by each other
N = P, that is, the number of columns of a should be equal to the number of rows of B
AB = C, then the element C (ij) in C is obtained by multiplying the i-th row in a by the j-th column in B

Algorithm and general solution of matrix multiplication
Does the algorithm of matrix multiplication have: a (B + C) = AB + AC?
Is there: (a + b) (a-b) = a ^ 2-AB + ba-b ^ 2?
After reading a lot of books and reference materials, I feel that sometimes the above formula is OK, but sometimes it is not. Why?
Also, given AB = 0 and B, how to find the general solution of AX = 0? Which part does this belong to? Maybe I haven't learned yet

(A+B)(A-B)=A^2-B^2=A^2-2AB+B^2
A × B is equal to 0, where either a or B has a number zero, because 0 × any number gets 0

Let a be a third-order matrix, and | a | = half, find the value of | (3a) ^ - 1 - 2A ^ * |

|（3A）^-1 - 2A*|
=|2∕3 x A*-2A*|
=| - 4∕3 A*|
=| - 4∕3 A*A|x1∕|A|
=|-2∕3E|x2
=(-2∕3)³×2
= -16／27