Two matrices are given:
A=[2−10345],B=[120−34−152]A = \begin{bmatrix} 2 & -1 \\ 0 & 3 \\ 4 & 5 \end{bmatrix}, \qquad B = \begin{bmatrix} 1 & 2 & 0 & -3 \\ 4 & -1 & 5 & 2 \end{bmatrix}A=204−135,B=[142−105−32]
The product ABABAB is formed. Write (AB)ij(AB)_{ij}(AB)ij for the entry sitting in row iii, column jjj of the result, with rows and columns counted from 1.
What is the shape of ABABAB, and what is the value of (AB)23(AB)_{23}(AB)23?
Select all that apply.
ABABAB is 3×43 \times 43×4, and (AB)23=3(AB)_{23} = 3(AB)23=3
ABABAB is 3×43 \times 43×4, and (AB)23=15(AB)_{23} = 15(AB)23=15
ABABAB is 4×34 \times 34×3, and (AB)23=15(AB)_{23} = 15(AB)23=15
ABABAB is 3×43 \times 43×4, and (AB)23=25(AB)_{23} = 25(AB)23=25