Prove that the following matrix A satisfies its characteristic equation `A=[[1,0,2],[0,2,1],[2,0,3]]`

Show that the matrix A=[2 3 1 2] satisfies the equation A^2-4A+I=0

The matrix A satisfying the equation [[1,3],[0,1]] A=[[1,1],[0,-1]], is________.

The matrix A satisfying the equation [(1,3),(0,1)]A=[(1,1),(0,1)] is

If matrix A satisfies the equation A^2+5A+6I=0 then A^3 is

If A is a square matrix of any order then |A-x|=0 is called the characteristic equation of matrix A and every square matrix satisfies its characteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-u)]=[(1-x,2),(1,5-x)] Characteristic equation of matri A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x0-2=0 or x^2-6x+3=0 Matrix A will satisfy this equation ie. A^2-6A+3I=0 A^-1 can be determined by multiplying both sides of this equation let A=[(1,0,0),(0,1,1),(1,-2,4)] ON the basis fo above information answer the following questions: |A^-1|= (A) 6 (B) 1/6 (C) 12 (D) none of these

The matrix A satisfying the equation [(1,3),(0,1)]A=[(1,1),(0,-1)] is

If A is a square matrix of any order then |A-x|=0 is called the characteristic equation of matrix A and every square matrix satisfies its characteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-u)]=[(1-x,2),(1,5-x)] Characteristic equation of matri A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x0-2=0 or x^2-6x+3=0 . Matrix A will satisfy this equation ie. A^2-6A+3I=0 then A^-1 can be determined by multiplying both sides of this equation let A=[(1,0,0),(0,1,1),(1,-2,4)] On the basis fo above information answer the following questions: If 6A^-1=A^2+aA+bI, then (a,b) is (A) (-6,11) (B) (-11,60 (C) (11,6) (D) (6,11)

If A is a square matrix of any order then |A-x|=0 is called the characteristic equation of matrix A and every square matrix satisfies its characteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-u)]=[(1-x,2),(1,5-x)] Characteristic equation of matri A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x0-2=0 or x^2-6x+3=0 . Matrix A will satisfy this equation ie. A^2-6A+3I=0 then A^-1 can be determined by multiplying both sides of this equation let A=[(1,0,0),(0,1,1),(1,-2,4)] On the basis fo above information answer the following questions: If 6A^-1=A^2+aA+bI, then (a,b) is (A) (-6,11) (B) (-11,60 (C) (11,6) (D) (6,11)

If A is a square matrix of any order then |A-x|=0 is called the chracteristic equation of matrix A and every square matrix satisfies its chatacteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-x)]=[(1-x,2),(1,5-x)] Characteristic equation of matrix A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x)(0-2)=0 or x^2-6x+3=0 Matrix A will satisfy this equation ie. A^2-6A+3I=0 . A^-1 can be determined by multiplying both sides of this equation. Let A=[(1,0,0),(0,1,1),(1,-2,4)] On the basis for above information answer the following questions:Sum of elements of A^-1 is (A) 2 (B) -2 (C) 6 (D) none of these