Algebra
Determinant Evaluation
MMTS_Full_Test_11
Grade 12
Question:
The value of $\begin{vmatrix}1+a^2-b^2&2ab&-2b\\2ab&1-a^2+b^2&2a\\2b&-2a&1-a^2-b^2\end{vmatrix}$ is
$(1+a^2+b^2)^3$
$(1+a^2+b^2)^2$
$(1+a^2+b^2)$
$0$
Step-by-Step Solution
Key Concept: This determinant equals $(1+a^2+b^2)^3$
$(1+a^2+b^2)^3$.
Correct Answer: 3