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

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 ?...

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

If the lines and are coplanar, then k can have :

If is the adjoint of a 3 × 3 matrix A and |A| = 4, then α is equal to

Let. If u1 and u2 are column matrices such that and then u1 + u2 is equal to :...

Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form , where each of a, b, and c is either ω or ω2. Then the number of distinct matrices in ...

Let P = [aij] be a 3 × 3 matrix and let Q = [bij], where bij = 2i + jaij for 1 ≤ i, j ≤ 3. If the determinant of P is 2, then the determinant of the matrix Q is...

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

If A and B are square matrices of order 5 such that A2 + B4 = (AT)2, then det(B) is (where AT is transpose of matrix A) -...

Let matrix A = , where x, y, z ∈ N. If det.(Adj(AdjA)) = 28.34, then total number of such matrices A, is -...

Matrices are formed using four given distinct real numbers, taking all at a time, of all possible orders. Number of such distinct possible matrices is -