If two matrices contain the same numbers as elements, are the two matrices equal to each other?
No, to be equal, two matrices must have the same dimensions, and must have the same values in the same positions.
For two matrices to be equal, they must have
In other words, say that
Then A = B if and only if n=p, m=q, and aij=bij for all i and j in range.
Here are two matrices which are not equal even though they have the same elements.