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The number of elements in a 3 X 3 matrix is the product 3 X 3=9.
Each element can either be a 0 or a 1.
Given this, the total possible matrices that can be selected is 29=512
The number of elements in a 2 x 2 matrix is the product 2 x 2 =4
Each element can either be a 0,1 or 2.
Given this, the total possible matrices that can be selected is 34
A square matrix A for which, where n is a positive integer, is called a Nilpotent matrix.
The determinant and trace of the matrix is always Zero for a Nilpotent Matrix.
For the given matrix "A", determinant (A)=0 and trace(A)=0.
Only a null matrix can be symmetric as well as skew symmetric.
In Symmetric Matrix AT =A,
Skew Symmetric Matrix AT = -A,
Given that the matrix is satisfying both the properties therefore Equating the RHS we get A= -A i.e 2A=0 .
Therefore A=0,which is a null matrix.