If A is an invertible matrix of order 2, then (( adj A)^(-1)) is equal to Option 1: 0 Option 2: 1 Option 3: A Option 4: 1/( A)

Answer: 1/( A). Solution: For any invertible matrix B: (B^(-1)) = 1/((B)) For a matrix A of order n: (adj A) = ( A)^(n-1) Since A is a 2×2 matrix (order 2): (adj A) = ( A)^(2-1) (adj A) = ( A)^1 (adj A) = A Applying the inverse determinant property: ((adj A)^(-1)) = 1/((adj A)) Substituting the value from above: ((adj A)^(-1)) = 1/( A) Therefore, ((adj A)^(-1)) = 1/( A)

Algebra

Matrices & Determinants

Medium

common

If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to

$\det A$

$\frac{1}{\det A}$

✅ Correct Option: 4

For any invertible matrix B:

$\det(B^{-1}) = \frac{1}{\det(B)}$

For a matrix A of order n:

$\det(\text{adj } A) = (\det A)^{n-1}$

Since A is a 2×2 matrix (order 2):

$\det(\text{adj } A) = (\det A)^{2-1}$

$\det(\text{adj } A) = (\det A)^{1}$

$\det(\text{adj } A) = \det A$

Applying the inverse determinant property:

$\det((\text{adj } A)^{-1}) = \frac{1}{\det(\text{adj } A)}$

Substituting the value from above:

$\det((\text{adj } A)^{-1}) = \frac{1}{\det A}$

Therefore, $\det((\text{adj } A)^{-1}) = \dfrac{1}{\det A}$

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CUET Mathematics Past Year Questions (Topic-Wise)

If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to