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

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

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

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 satisfying the equation A^(2)-4A-5I=0 , then A^(-1)=

The solution set of the equation |{:(1,4,20),(1,-2,5),(1,2x,5x^(2)):}|=0 is

The solution set of the equation |{:(1,4,20),(1,-2,5),(1,2x,5x^(2)):}|=0 is

The solution of matrix equation [{:(x,1):}][{:(1,0),(-2,0):}]=O is 5 .

Solve the matrix equation [(2,1),(5,0)]-3X=[(-7,4),(2,6)]