Matrix Multiplication Calculator
Note: Matrices multiplication is possible only when the number of columns of first matrix is equal to the number of rows of second matrix. For example: (3x2)*(2x3), (3x3)*(3x1).
In the multiplication of two matrices we multiply row elements in Matrix-1 (A) by corresponding column elements in Matrix-2 (B).
The matrix multiplication is defined for AB. We can not say BA because results may be different.
Therefore AB is not always equal to BA. The order matters in the case multiplication of two matrices.
We can multiply matrices if the number of columns of the first matrix is the same as the number of rows as the second matrix.
For example:
\[ \begin{bmatrix} 11 & 12 & 13\\ 21 & 22 & 23\\ 31 & 32 & 33 \end{bmatrix} \times \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{bmatrix} \] \[= \begin{bmatrix} (11*1)+(12*4)+(13*7) & (11*2)+(12*5)+(13*8) & (11*3)+(12*6)+(13*9) \\ (21*1)+(22*4)+(23*7) & (21*2)+(22*5)+(23*8) & (21*3)+(22*6)+(23*9) \\ (31*1)+(32*4)+(33*7) & (31*2)+(32*5)+(33*8) & (31*3)+(32*6)+(33*9) \end{bmatrix}\] \[= \begin{bmatrix} 150 & 186 & 222\\ 270 & 336 & 402\\ 390 & 486 & 582 \end{bmatrix} \]
\[ \begin{bmatrix} 11 & 12 & 13\\ 21 & 22 & 23\\ 31 & 32 & 33 \end{bmatrix} \times \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{bmatrix} \] \[= \begin{bmatrix} (11*1)+(12*4)+(13*7) & (11*2)+(12*5)+(13*8) & (11*3)+(12*6)+(13*9) \\ (21*1)+(22*4)+(23*7) & (21*2)+(22*5)+(23*8) & (21*3)+(22*6)+(23*9) \\ (31*1)+(32*4)+(33*7) & (31*2)+(32*5)+(33*8) & (31*3)+(32*6)+(33*9) \end{bmatrix}\] \[= \begin{bmatrix} 150 & 186 & 222\\ 270 & 336 & 402\\ 390 & 486 & 582 \end{bmatrix} \]