For a square matrix A if A² – A + I = O then it means that the matrix satisfies the equation where A is the matrix itself and I is the identity matrix. This equation can be used to analyze the properties and behavior of the matrix A.
Chapter 4 of Class 12 Maths covers Determinants. It teaches methods like cofactor expansion to calculate determinants and explains their properties. The chapter also discusses applications such as solving linear equations using Cramer’s rule and finding the inverse of matrices. Mastering these concepts is important for the CBSE Exam 2024-25.
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We have the equation of a square matrix A as
A² – A + I = O
Rearrange the equation to get
A² – A = -I
Now we factor the left-hand side,
A(A – I) = -I
To get the inverse of A (A⁻¹), multiply both sides of the equation by A⁻¹,
A⁻¹ * A(A – I) = A⁻¹ * (-I)
This gives us,
(A – I) = -A⁻¹
Thus we can write
A⁻¹ = I – A
Hence, the correct answer is option (c) I – A.
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