Matrices & Determinants
Matrix Powers
MMTS_Full_Test_19
Grade 12
Question:
$A=\begin{bmatrix}1&-2\\0&1\end{bmatrix}$, $B=\begin{bmatrix}5&2\\2&1\end{bmatrix}$. Then $(ABA^T)^5(AB^TA^T)^{10}=X$. Then trace of matrix $X$ is
Step-by-Step Solution
Key Concept: Note $B=A^{-T}\cdot\text{something}$; compute product
$(ABA^T)^5(AB^TA^T)^{10}$: using $BB^T$ properties... trace $=4$.
Correct Answer: 1