If `A=([a_(i j)])_(nxxn)` is such that `( a )_(i j)=bar (a_(j i)),AAi ,j` and `A^2=O ,` then
Statement 1: Matrix `A` null matrix.
Statement 2: `|A|=0.`

Let A=[a_(ij)]_(mxxn) be a matrix such that a_(ij)=1 for all I,j. Then ,

If A=[a_(i j)] is a 2xx2 matrix such that a_(i j)=i+2j , write A .

A =([a_(i j)])_(mxxn) is a square matrix, if (a) m n (c) m =n (d) None of these

If A=[a_(i j)] is a 3xx3 diagonal matrix such that a_(11)=1 , a_(22)=2 and a_(33)=3 , then find |A| .

If A=[a_(i j)] is a square matrix such that a_(i j)=i^2-j^2 , then write whether A is symmetric or skew-symmetric.

Statement 1: The inverse of singular matrix A=([a_(i j)])_(nxxn), \ w h e r e \ a_(i j)=0,igeqj \ i s \ B=([a i j^-1])_(nxxn) . Statement 2: The inverse of singular square matrix does not exist.

If matrix A = [a_(i j)]_(2 xx 2) , where a_(i j) = {("1 if",i ne j),("0 if",i = j):} then A^(2) is equal to

Let A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.

If A=[a_(i j)] is a 3xx3 scalar matrix such that a_(11)=2 , then write the value of |A| .

If matrix A=([a_(i j)])_(2xx2) , where a_(i j)={1,\ if\ i!=j0,\ if\ i=j , then A^2 is equal to I (b) A (c) O (d) I