Find (if possible) a. $A B$ and $b . B A$, if $A=\left[\begin{array}{rr}-3 & -2 \\ -4 & 4 \\ -5 & -2\end{array}\right], B=\left[\begin{array}{rrr}2 & 5 & -5 \\ -2 & -1 & -5\end{array}\right]$.
Answer
Final Answer: The product of matrix A and B is \(\boxed{\left[\begin{array}{rrr}-2 & -13 & 25 \\ -16 & -24 & 0 \\ -6 & -23 & 35\end{array}\right]}\). The product of matrix B and A is not possible because the number of columns in B is not equal to the number of rows in A.
Step 1 ：Given matrices A and B as \(A=\left[\begin{array}{rr}-3 & -2 \\ -4 & 4 \\ -5 & -2\end{array}\right]\) and \(B=\left[\begin{array}{rrr}2 & 5 & -5 \\ -2 & -1 & -5\end{array}\right]\).
Step 2 ：We are asked to find the product of A and B, and B and A.
Step 3 ：In matrix multiplication, the number of columns in the first matrix should be equal to the number of rows in the second matrix.
Step 4 ：Matrix A is a 3x2 matrix and matrix B is a 2x3 matrix. So, we can multiply A and B.
Step 5 ：But, B and A cannot be multiplied because the number of columns in B is not equal to the number of rows in A.
Step 6 ：Calculating the product of A and B, we get \(A B = \left[\begin{array}{rrr}-2 & -13 & 25 \\ -16 & -24 & 0 \\ -6 & -23 & 35\end{array}\right]\).
Step 7 ：Final Answer: The product of matrix A and B is \(\boxed{\left[\begin{array}{rrr}-2 & -13 & 25 \\ -16 & -24 & 0 \\ -6 & -23 & 35\end{array}\right]}\). The product of matrix B and A is not possible because the number of columns in B is not equal to the number of rows in A.
