Then sum of the products of the elements of any row of a determinant A with the co-factors of the corresponding elements is equal to
1
0
|A|
1/2 [A]
Let the determinant of a 3 × 3 matrix A be 6, then B is a matrix defined by B = 5A2, then, determinant of B is
180
100
80
none of these
The adjoint of the matrix is
If A and B are square matrices of the same order such that (A+B) (A-B) = A2 - B2, then (ABA-1)2 is equal to
B2
I
A2B2
A2
If A is a square matrix, then
A + AT is symmetric
AAT is skew - symmetric
AT + A is skew - symmetric
AT A is skew symmetric
The characteristic root of the matrix are
1,3,6
1,2,4
4,5,6
2,4,6
then A12 is.
The system of equations zx + y + z = 0; x + by + z = 0; x + y + cz = 0 has non- trivial solution, then
2
-1
If A is an invertible matrix of order n, then the determinant of adj (A) is equal to
|A|n
|A|n+1
|A|n-1
|A|n+2
The rank of the matrix is
3
4
