Question

if A be a square matrix of order 2 satisfying A^2-5A + 6I = O where I is the identity matrix of order 2. then which is incorrect [ Det(A) denotes the determination of the matrix A. Note A is satisfying the equation x^2-5x+6=0.].
(a)det(A)=6
(b)A is non-singular matrix
(c)Det(A) = 5
(d)A^{-1} exists​

Answer 1

Answer:

det a 6

Step-by-step explanation:

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Answer 2

Given:

• A be a square matrix of order 2 satisfying A^2-5A - 6I = O where I is the identity matrix of order 2.

To find:

• Which of the following is incorrect [ Det(A) denotes the determination of the matrix A. Note A is satisfying the equation x^2-5x+6=0.].
• (a)det(A)=6
• (b)A is non-singular matrix
• (c)Det(A) = 5
• (d)A^{-1} exists​

Solution:

• As given above, A satisfies $x^{2} -5x-6=0$ equation.
• so,
• $x^{2} -5x-6=0\\ or, x^{2} -6x+1-6=0\\ or,x(x-6)+1(x-6)=0\\ or,(x-6)(x+1)=0$
• so value of $x=6,-1$
• so, det(A)=6 and Det(A)= -1.
• Now, analysing the given options, we find,
• (a) det(A)=6 : is correct.
• (b) A is non-singular matrix: correct. as A has a value.
• (c) det(A)= 5: is incorrect. as det(A)= 6 or -1.
• (d) $A^{-1}$ exists: Insufficient information ( To find inverse of a matrix, the matrix element should be given)

Final answer:

the incorrect option is option (c): det(A)=5