Answer to Question #101838 in Matrix | Tensor Analysis for Kelbesa Gemechu

Question #101838
Suppose A is a square matrix such that det(A)= 2 and det(3At)= 18 then find the order of matrix A
1
Expert's answer
2020-01-30T09:12:53-0500

det(cA) = "c^n"det(A), where "n" is the dimension of the matrix (n rows, n columns).

det("A^T") = det(A) since transposing a matrix doesn't change its determinant.

So "det(3A^T)" = "3^ndet(A^T)=3^ndet(A)=3^n \\cdot 2=18, \\, 3^n=9," "\\,n=2."

Answer: the order of matrix "A" is 2.


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