DeterminantHard
Question
If A is a skew - symmetric matrix and n is an even positive integer, then An is
Options
A.a symmetric matrix
B.a skew-symmetric matrix
C.a diagonal matrix
D.none of these
Solution
AT = - A
(An)T = (AAA ------- A)T = (AT AT AT ------- AT) = (AT)n for all n ∈ N
(-A)n = (-1)n An
(An)T =
(An)T = (AAA ------- A)T = (AT AT AT ------- AT) = (AT)n for all n ∈ N
(-A)n = (-1)n An
(An)T =
Create a free account to view solution
View Solution FreeMore Determinant Questions
If A is a square matrix of order 3, then the true statement is (where I is unit matrix)....Let ᐃ = , then...The determinant is equal to zero, if -...The existence of unique solution of the system x + y + z = b, 2x + 3y − z = 6, 5x − y + az = 10 depends on -...If ᐃ1 = and ᐃ2 = are given, then-...