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To form a Sub-matrix , we have a choice for each row & column - to take or not to take. 

So, total we have 2* 2choices , 

But we have to exclude matrix having 0 rows & 0 columns -  which can be formed when we delete all rows OR All Columns , which correspond to  2+ 2n - 1 ways.

Let's see with an example - 

a

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CONSIDER THIS AS SUBSTRING PROBLEM

given (ab)=a,b,ab(these are possible substrings) =3 number of substrings=x(x+1)/2

but null not be considered as that would produce null matrix

SIMILARLY u can think column also as substring ...so when

M         X         N  matrix is given ...we have

{M(M+1)}/2     * {N(N+1)}/2= M(M+1)N(N+1)/4 in total

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