Strassen’s matrix is a Divide and Conquer method that helps us to multiply two matrices(of size n X n).

You can refer to the link, for having the knowledge about Strassen’s Matrix first :

Divide and Conquer | Set 5 (Strassen’s Matrix Multiplication)

But this method needs to cram few equations, so I’ll tell you the simplest way to remember those :

You just need to remember 4 Rules :

- AHED (Learn it as ‘Ahead’)
- Diagonal
- Last CR
- First CR

Also, consider X as (Row +) and Y as (Column -) matrix

Follow the Steps :

- Write P1 = A; P2 = H; P3 = E; P4 = D
- For P5 we will use Diagonal Rule i.e.

(Sum the Diagonal Elements Of Matrix X ) * (Sum the Diagonal Elements Of Matrix Y ), we get

P5 = (A + D)* (E + H) - For P6 we will use Last CR Rule i.e. Last Column of X and Last Row of Y and remember that Row+ and Column- so i.e. (B – D) * (G + H), we get

P6 = (B – D) * (G + H) - For P7 we will use First CR Rule i.e. First Column of X and First Row of Y and remember that Row+ and Column- so i.e. (A – C) * (E + F), we get

P7 = (A – C) * (E + F)

P1 = A

P2= H

P3= E

P4= D

P5= ( A + D ) * ( E + H )

P6= ( B – D ) * ( G + H)

P7= ( A – C ) * ( E + F) - Come Back to P1 : we have A there and it’s adjacent element in Y Matrix is E, since Y is Column Matrix so we select a column in Y such that E won’t come, we find F H Column, so multiply A with (F – H)

So, finally P1 = A * (F – H)

P1 = A * ( F – H)

P2= H

P3= E

P4= D

P5= ( A + D ) * ( E + H )

P6= ( B – D ) * ( G + H)

P7= ( A – C ) * ( E + F) - Come Back to P2 : we have H there and it’s adjacent element in X Matrix is D, since X is Row Matrix so we select a Row in X such that D won’t come, we find A B Column, so multiply H with (A + B)

So, finally P2 = (A + B) * H - Come Back to P3 : we have E there and it’s adjacent element in X Matrix is A, since X is Row Matrix so we select a Row in X such that A won’t come, we find C D Column, so multiply E with (C + D)

So, finally P3 = (C + D) * E

P1= A * ( F – H )

P2= H * ( A + B )

P3= E * ( C + D )

P4= D

P5= ( A + D ) * ( E + H )

P6= ( B – D ) * ( G + H)

P7= ( A – C ) * ( E + F) - Come Back to P4 : we have D there and it’s adjacent element in Y Matrix is H, since Y is Column Matrix so we select a column in Y such that H won’t come, we find G E Column, so multiply D with (G – E)

So, finally P4 = D * (G – E)We are done with P1 – P7 equations, so now we move to C1 – C4 equations in Final Matrix C :

- Remember Counting : Write P1 + P2 at C2
- Write P3 + P4 at its diagonal Position i.e. at C3
- Write P4 + P5 + P6 at 1st position and subtract P2 i.e. C1 = P4 + P5 + P6 – P2
- Write odd values at last Position with alternating – and + sign i.e. P1 P3 P5 P7 becomes

C4 = P1 – P3 + P5 – P7

This article is contributed by **Mohit Gupta 🙂**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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