A=[123−1]A = \begin{bmatrix} 1 & 2 \\ 3 & -1 \end{bmatrix}A=[132−1]
Here A3A^3A3 means the matrix product A⋅A⋅AA \cdot A \cdot AA⋅A⋅A — three copies of AAA multiplied together, using matrix multiplication each time.
Compute A3A^3A3.
Suggestion: work out A2A^2A2 completely and look hard at what you get before charging into the third multiplication.
Select all that apply.
[1827−1]\begin{bmatrix} 1 & 8 \\ 27 & -1 \end{bmatrix}[1278−1]
[13−21217]\begin{bmatrix} 13 & -2 \\ 12 & 17 \end{bmatrix}[1312−217]
[71421−7]\begin{bmatrix} 7 & 14 \\ 21 & -7 \end{bmatrix}[72114−7]
[714217]\begin{bmatrix} 7 & 14 \\ 21 & 7 \end{bmatrix}[721147]