$\mathit{A}=\left[\begin{array}{ccc}1& -2& -1\\ 0& 4& -1\\ -3& 2& 1\end{array}\right],\mathit{B}=\left[\begin{array}{c}-2\\ -5\\ -7\end{array}\right],\mathit{C}=\left[9,8,7\right]$
Order of A is $3\times 3$
Order of B is $3\times 1$
Order of C is $1\times 3$
Product of two matrices A and B is defined if the number of columns in matrix A is equal to number of rows in matrix B.
No. of column of matrix A = no. of rows of matrix B
∴ A B is defined
No. of column of matrix A = 3
∴ no. of row of matrix C = 1
∴ A C is not defined.
No. of column of matrix B is not equal to no. of rows matrix A.
So, BA is not defined.
No. of column of A is not equal to no. of row of C
∴ A C is not defined