Let `A=([a_(i j)])_(3x3)` be a matrix such that `a_(11)=a_(33)=2` and all the other elements`a_(i j)=1 A^(-1)=`
(a)`A^2+5A-I`
(b) `A^2-5A+5I`
(c)`A^2+5A-5I`
(d) `A^2+5A+5I`

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

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 2xx2 matrix such that a_(i j)=i+2j , write 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.

Let a_(1),a_(2)…,a_(n) be a non-negative real numbers such that a_(1)+a_(2)+…+a_(n)=m and let S=sum_(iltj) a_(i)a_(j) , then

Construct a 3 xx2 matrix whose elements are given by a_(i j)=j-i .

Construct a 3 xx2 matrix whose elements are given by a_(i j)=1/2|i-3j| .

Construct a 3 xx 2 matrix whose elements ar given by a_(ij)=(1)/(2)(i-3j)

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 _______.

Construct a 2xx3 matrix A=[a_(i j)] whose elements are given by a_(i j)=(1-j)/(1+i)