`A=[(0,1),(3,0)]` and `A^(8)+A^(6)+A^(4)+A^(2)+I V=[(0),(11)]` (where `I` is the`2xx2` idensity matrix), then the product of all elements of matrix V is _________.

A=[0 1 3 0]a n dA^8+A^6+A^2+I V=[0 11](w h e r eIi s the 2xx2 identity matrix ), then the product of all elements of matrix V is _____.

Let A=[(0,1),(0,0)] , show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA , where I is the identity matrix of order 2 and n in N .

If A= ((2,3),(-1,2)) .Show that A^(2)-4A+7I=0 whwre I is the unit matrix of order 2.

If A = [(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying the equation "AA"^(T) = 9I , where I is 3xx3 identity matrix, then the ordered pair (a,b) is equal to

If A= [(3,4),(4,-3)] find x if det|A-xI| =0,where I is a unit matrix of order 2.

If [2-1 1 0-3 4]A=[-1-8-10 1-2-5 9 22 15] , then sum of all the elements of matrix A is 0 b. 1 c. 2 d. -3

Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r for which A=[I^2-3p0 0m^2-8q r0n^2-15] be non-singular idempotent matrix. Then the sum of all the elements of the set S is ________.

Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r for which A=[I^2-3p0 0m^2-8q r0n^2-15] be non-singular idempotent matrix. Then the sum of all the elements of the set S is ________.

A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P^(n)=5I-8P , then n is