Matrices Questions

If A is an 3 × 3 non-singular matrix such that AA′ = A′A and B = A-1A′, then BB′ equals

For 3 × 3 matrices M and N, which of the following statement(s) is (are) NOT correct ?

Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if

Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠ N and M2 = N2, then

Which of the following is(are) NOT the square of a 3 ×3 matrix with real entries ?

Let X and Y be two arbitrary, 3 × 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 × 3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric ?...

If P is a 3 × 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 × 3 identity matrix, then there exists a column matrix X = such that...

The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

The number of 3 × 3 matrices A whose entries are either 0 or 1 and for which the system A has exactly two distinct solutions, is...

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

If A and B are square matrices of size n × n such that A2 − B2 = (A - B) (A + B), then which of the following will be always true ?

Let A = . If B is the inverse of matrix A, then $\alpha$ is

A and B are two matrices with 32 and 40 elements respectively, then the probability that (A × B) is possible is :-

Median and mode of a moderately Skew symmetric distribution is 13 and 7 respectively then mean of the distribution will be :-

Matrix A = , if xyz = 50 and 8x + 4y + 3z = 30 then A (adj A) is equal to:-

If the matrices A, B, (A + B) are non-singular (where A and B are of same order), then (A(A+B)-1B)-1 is equal to -

If A is a matrix of order 3 × 4, then each row of A has -

In the following, upper triangular matrix is -

In the following, singular matrix is -

If A = and B = , then | 2A − 3B | equals -...