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The identity matrix of order n is denoted by I∩

It is a square matrix with dimensions n×nn×n where all the elements on the main diagonal (from the top left to the bottom right) are 1, and all other elements are 0.

To find the number of all possible matrices of order 3×33×3 with each entry being either 0 or 1, we can consider that each entry in the matrix has 2 choices (0 or 1), and there are a total of 3×3=93×3=9 entries in the matrix.

Therefore, the total number of possible matrices is 2929, because for each entry, there are 2 choices, and we multiply these choices together for all 9 entries.

So, the number of all possible matrices of order 3×33×3 with each entry being either 0 or 1 is 29=51229=512.

Two matrices A=[aij]A=[aij] and B=[bij]B=[bij] are said to be equal if they have the same dimensions (i.e., the same number of rows and columns) and if each corresponding entry of matrix AA is equal to the corresponding entry of matrix BB.

Formally, two matrices AA and BB are equal if and only if:

1. They have the same dimensions, meaning they both have the same number of rows and the same number of columns.
2. For each ii and jj, aij=bijaij=bij, where aijaij represents the entry in the ii-th row and jj-th column of matrix AA, and bijbij represents the entry in the ii-th row and jj-th column of matrix BB.

In other words, matrices AA and BB are equal if they have the same size and if the corresponding entries in each position are equal.