" (i) "-1" and "0

Which of the following is (are) NOT the square of a 3xx3 matrix with real entries? [1 0 0 0 1 0 0 0-1] (b) [-1 0 0 0-1 0 0 0-1] [1 0 0 0 1 0 0 0 1] (d) [1 0 0 0-1 0 0 0-1]

Let, I=({:(1,0,0),(0,1,0),(0,0,1):}) " and " P=({:(1,0,0),(0,-1,0),(0,0,-2):}) . Then the matrix P^(3)+2P^(2) is equal to -

[(1,3,-2),(-3,0,-5),(2,5,0)] =A [(1,0,0),(0,1,0),(0,0,1)] then, C_(2) rarr C_(2)-3C_(1) and C_(3) rarr C_(3) +2C_(1) gives... [(1,0,0),(3,-9,11),(-2,1,4)] =A [(-1,3,2),(0,-1,0),(0,0,-1)] [(1,0,0),(-3,-1,-4),(2,-9,11)] =A [(1,-3,2),(0,1,0),(0,0,1)] [(1,0,0),(-3,1,4),(-2,9,-11)] =A [(-1,3,2),(0,-1,0),(0,0,-1)] [(1,0,0),(-3,9,-11),(2,-1,4)] =A [(1,-3,2),(0,1,0),(0,0,1)]

If [[2" "1" "3][{:(-1,0,-1),(-1,1,0),(0,0,1):}]*[{:(1),(0),(-1):}]=A find A.

If A = [ [ 0 , 1 ] , [ 0 , 1 ] ] ,then A^2 is equal to ( a ) [ [ 0 , 1 ] , [ 1 , 0 ] ] ( b ) [ [ 1 , 0 ] , [ 1 , 0 ] ] ( c ) [ [ 0 , 1 ] , [ 0 , 1 ] ] ( d ) [ [ 1 , 0 ] , [ 0 , 1 ] ]

Which of the following matrices have eigen values as 1 and -1 ? (a) [(0,1),(1,0)] (b) [(0,1),(1,0)] (c) [(1,0),(0,-1)] (d) [(1,0),(0,1)]

(i) {:[( 1,0,0),( 0,1,0),( 0,0,1) ]:}" "(ii) {:[( 1,0,4),(3,5,-1),( 0,1,2) ]:}