Matrices

Concept:Matrix multiplication $BA$ is defined when the number of columns in $B$ equals the number of rows in $A$.Explanation:Given $A = \begin{bmatrix} 1 & -1 & 1 \\ -3 & 2 & -1 \\ -2 & 1 & 0 \end{bmatrix}$ (assuming the dot is a typo for $2$) and $B = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 1 & 2 & 3 \end{bmatrix}$.Compute each entry of $BA$ by dot product of rows of $B$ and columns of $A$.First row of $B$: $[1,2,3]$.• Column 1: $1(1) + 2(-3) + 3(-2) = 1 - 6 - 6 = -11$.• Column 2: $1(-1) + 2(2) + 3(1) = -1 + 4 + 3 = 6$.• Column 3: $1(1) + 2(-1) + 3(0) = 1 - 2 + 0 = -1$.Second row of $B$: $[2,4,6]$.• Column 1: $2(1) + 4(-3) + 6(-2) = 2 - 12 - 12 = -22$.• Column 2: $2(-1) + 4(2) + 6(1) = -2 + 8 + 6 = 12$.• Column 3: $2(1) + 4(-1) + 6(0) = 2 - 4 + 0 = -2$.Third row of $B$: $[1,2,3]$ (same as first) gives $[-11, 6, -1]$.Thus $BA = \begin{bmatrix} -11 & 6 & -1 \\ -22 & 12 & -2 \\ -11 & 6 & -1 \end{bmatrix}$.Answer:Option B.