If n times n matrix A is multiplied by a scalar c, the determinant of the result

Question

If n times n matrix A is multiplied by a scalar c, the determinant of the resulting matrix is cn det (A). If two rows of an n times n matrix are interchanged, the first row is multiplied by 3 and the third row is multiplied by 1/3, then the value of the determinant is unchanged. If C and A are n times n matrices and C is an invertible matrix then Det (C -1 (AC) = det (A) If det (A) = 2 and det (B) = 3 then det (AB) = 6 The determinant of a 3 Times 3 matrix is zero if the points in R 3 given by the rows of the matrix lie in a plane.

Explanation / Answer

a is true

b is true

c is true

d is true det (AB) = det(A) det(B)

e is true

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