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No, to be equal, two matrices must have the same dimensions, and must have the same values in the same positions.

Matrix Equality

For two matrices to be equal, they must have

  1. The same dimensions.
  2. Corresponding elements must be equal.

In other words, say that An x m = [aij] and that Bp x q = [bij].

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.

Unequal Matrices


Here is another pair of matrices.

Possibly unequal matrices

Are these two matrices equal?