Statement - 1: Determinant of a skew-symmetric matrix of order 3 is zero. Statement - 2: For any matrix A, det (A)T = det (A) and det (- A) = - det (A). Where det (B) denotes the determinant of matrix B. Then :

Question

Statement - 1: Determinant of a skew-symmetric matrix of order 3 is zero. Statement - 2: For any matrix A, det (A)T = det (A) and det (- A) = - det (A). Where det (B) denotes the determinant of matrix B. Then : (A) Both statements are true (B) Both statements are false (C) Statement-1 is false and statement-2 is true (D) Statement-1 is true and statement-2 is false

Tardigrade Admin · Accepted Answer

Statement - 1: Determinant of skew symmetric matrix of odd order is zero. Statement - 2: det (A)T = det (A) . det (- A) = - (-1)n det (A). where A is a n × n order matrix.

Q. Statement - 1: Determinant of a skew-symmetric matrix of order 3 is zero.
Statement - 2 : For any matrix A, det $(A)^{T}$ = det (A) and det (- A) = - det (A). Where det (B) denotes the determinant of matrix B. Then :

Both statements are true

Both statements are false

Statement-1 is false and statement-2 is true

Statement-1 is true and statement-2 is false

Statement - 1: Determinant of skew symmetric matrix of odd order is zero.
Statement - 2 : det $(A)^{T}$ = det (A) .
det (- A) = - $(- 1)^{n}$ det (A). where A is a $n \times n$ order matrix.

Q. Statement - 1: Determinant of a skew-symmetric matrix of order 3 is zero. Statement - 2 : For any matrix A, det (A)T = det (A) and det (- A) = - det (A). Where det (B) denotes the determinant of matrix B. Then :