Question

perform the matrix multiplication, if possible.
cannot be multiplied, dimensions not compatible.

Explanation:

Step1: Verify matrix compatibility

First matrix: $3 \times 2$, second matrix: $2 \times 2$. Columns of first = rows of second, so multiplication is possible. Result is $3 \times 2$ matrix.

Step2: Calculate first row elements

First row, first column: $(0)(3)+(3)(2)=0+6=6$
First row, second column: $(0)(-5)+(3)(3)=0+9=9$

Step3: Calculate second row elements

Second row, first column: $(1)(3)+(-3)(2)=3-6=-3$
Second row, second column: $(1)(-5)+(-3)(3)=-5-9=-14$

Step4: Calculate third row elements

Third row, first column: $(3)(3)+(-3)(2)=9-6=3$
Third row, second column: $(3)(-5)+(-3)(3)=-15-9=-24$

Answer:

$$\begin{bmatrix} 6 & 9 \\ -3 & -14 \\ 3 & -24 \end{bmatrix}$$