If A and B are square matrices of order 3 × 3, then which of the following is true?
AB = 0 ⇒ A = 0 or B = 0
det (2 AB) = 8 det (A) det (B)
A2 - B2 = (A+B) (A-B)
det (A+B) = det (A) + det (B)
If A and B are any two matrices that AB = 0 and A is non- singular, then
B = 0
B is singular
B is non singular
B =A
The rank of the matrix is.
1
2
3
4
Inverse of is.
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 inverse of is.
Does not exit
If A is a square matrix, A' is its transpose, then 1/2 ( A-A' ) is
a symmetric matrix
skew symmetric matrix
a unit matrix
an elementary matrix
If a ≠ b ≠ c, the value of x which satisfies the equation is.
x = 0
x = a
x = b
x = c
The system of equations zx + y + z = 0; x + by + z = 0; x + y + cz = 0 has non- trivial solution, then
-1
0
AB does not exist
