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What are the maximum number of distinct entries that are possible in a Skew Symmetric Matrix of Order n?

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Important Questions on Matrices and Determinants

MEDIUM
Let A  and B be any two 3×3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?
HARD
Let A=23a0, aR be written as P+Q where P is a symmetric matrix and Q is skew symmetric matrix. If detQ=9, then the modulus of the sum of all possible values of determinant of P is equal to:
HARD
Let A=0-220. If M and N are two matrices given by M=k=110 A2k and N=k=110 A2k-1 then MN2 is
EASY
If A,B are symmetric matrices of the same order, then AB-BA is a
EASY
If A and B are square matrices of same order and B is a skew symmetric matrix, then A'BA is
HARD
Let M be a 2×2 symmetric matrix with integer entries. Then M is invertible if
EASY

Let A=aij is a square matrix of order 2 where aij=i2-j2. Then A is

EASY
If A=5ab0 and A is symmetric matrix, show that a=b.
MEDIUM
Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2 is 1, then the possible number of such matrices is:
EASY

In a third order matrix A, aij denotes the element in the ith row and jth column.

If aij=0 for i=j
        =1 for i>j
        =-1 for i<j

Then the matrix is

EASY
Let A and B be any two 3 × 3  matrices. If A is symmetric and B is skew symmetric, then the matrix AB-BA is 
EASY
If the matrix A=0a-320-1b10  is skew symmetric, find the values of a and b.
HARD
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 ?
EASY
A square matrix A is said to be skew-symmetric, if A'=_____
HARD
Express the following matrix as the sum of a symmetric and a skew symmetric matrix:33-1-2-21-4-52,
MEDIUM
Show that A+A' is symmetric matrix, if A=2435
MEDIUM
If A and B are symmetric matrices of same order and X=AB+BA and Y=AB-BA, then XYT is equal to
MEDIUM
If P and Q are symmetric matrices of the same order, then PQ-QP is
EASY
If the matrix 235-1=A+B, where A is symmetric and B is skew-symmetric then B is equal to