Matrices & Determinants
Matrix multiplication
Grade 12
Question:
<p>If \(\det(A)\)=k, then det((A\)^0)^{-1}\cdotA) equals:</p>
<p>(A) k</p>
<p>(B) 1</p>
<p>(C) k^2</p>
<p>(D) 0</p>
Step-by-Step Solution
Key Concept: (A$^0)^{-1} = $I$ \Rightarrow $I$\cdotA = $A$.
1. $A$^0 = $I$ \Rightarrow $I$^{-1} = $I$
2. $I$\cdotA = $A$
3. $\det(A)$=k
Correct Answer: 1