Home › Maharashtra HSC Class 12 (Commerce) › businessmathematics › Matrices › If A is invertible, then A × A⁻¹ equals
If A is invertible, then A × A⁻¹ equals
AZero matrix (typical)
BIdentity matrix
CA (typical) (typical)
DA⁻¹ (typical)
Answer & Solution
Correct answer: B. Identity matrix
1. By definition, the inverse satisfies A × A⁻¹ = A⁻¹ × A = I (identity matrix).
2. Inverse exists only when |A| ≠ 0.
3. I has 1s on diagonal and 0s elsewhere.
4. Hence (B) is correct.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 1 "Matrices", §1.2 ¶§1.2_
Related questions
If A is a 3×3 matrix with det(A) = 5, then det(2A) isDeterminant of a 2×2 matrix [[a,b],[c,d]] equalsA matrix with the same number of rows and columns is calledIf A is invertible 2 × 2 and A² = I then A isDeterminant of a triangular matrix equalsA square matrix A is called symmetric ifIf A and B are square matrices of same order, in generalIf A is a 2 × 2 matrix with det(A) = d, then A^{-1} exists provided