# Can you multiply a 2x2 matrix by a 3x3 matrix?

Mar 17, 2018

No, these matrices are not compatible.

#### Explanation:

The first number represents the number of rows while the second indicates the number of columns.

For adding and subtracting, matrices have to have identical formats,

For multiplication, the number of columns of the first matrix must be the same as the number of rows of the second.

So a $2 \text{ x } \textcolor{b l u e}{3}$ matrix and a $\textcolor{b l u e}{3} \text{ x } 2$ matrix would be compatible

The answer would be a $2 \text{ x } 2$ matrix

Mar 17, 2018

No

#### Explanation:

We can only multiply two matrices $A$ and $B$ if the number of columns in $A$ is equal to the number of rows in $B$.

Obviously $2 \ne 3$ so we can't multiply a $2 \times 2$ matrix with a $3 \times 3$ matrix.

Mar 17, 2018

If you have, say, a×b and c×d matrices, you can multiply them only when $b = c$. If you were to multiply c×d matrix by a×b, then $d$ must equal $a$. Since $2 \ne 3$, you cannot multiply the two matrices.