Matrices & Determinants
Adjoint matrix; determinant of AB+2I
MJMT_Full_Test_02
Grade 12
Question:
If $A = \begin{bmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{bmatrix}$ and $B$ is the adjoint of $A$, then $\det(AB+2I)$ is (where $I$ is $3\times3$ identity)
Step-by-Step Solution
Key Concept: Use $AB=|A|\cdot I$ (since $A\cdot\text{adj}(A)=|A|I$). Then $AB+2I=(|A|+2)I$.
$|A|=1$, $AB+2I=3I$, $\det=27$.
Correct Answer: 1