Question
Download Solution PDFIf A is a 3×3 square matrix such that |A| = 4, then find the value of |A × adj(A)|.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Determinants:
- For two invertible matrices A and B, we have: det(A × B) = det(A) × det(B), which can also be written as |A × B| = |A| × |B|.
- |adj(A)| = |A|n - 1, where n is the order of the square matrix A.
Calculation:
We know that |adj(A)| = |A|n - 1, where n is the order of the square matrix A.
Now, |A × adj(A)| = |A × |A|n - 1| = |A|n.
The order of the given matrix A is n = 3 and |A| = 4.
∴ |A × adj(A)| = |A|n = 43 = 64.
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