For any invertible matrix A, which of the following is NOT true. Option 1: A, ≠ 0 Option 2: (A')^(-1) = (A^(-1))' Option 3: (adjA)^(-1) =, A, A Option 4: A^(-1), =, A, ^(-1)

Answer: (adjA)^(-1) =, A, A. Solution: Since adj A=, A, A^(-1), its inverse is A/(, A, ), not, A, A. The other three statements hold for every invertible matrix, so option 3 is the false one.

Algebra

Matrices & Determinants

Medium

core

For any invertible matrix $A$ , which of the following is NOT true.

$|A| \neq 0$

$(A')^{-1} = (A^{-1})'$

$(adjA)^{-1} = |A|A$

$|A^{-1}| = |A|^{-1}$

✅ Correct Option: 3

Since $adj\,A=|A|A^{-1}$ , its inverse is $\frac{A}{|A|}$ , not $|A|A$ . The other three statements hold for every invertible matrix, so option 3 is the false one.

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Match List-I with List-II

List-I	List-II
(Matrix A)	(Determinant of adj A)
(A) $\begin{bmatrix} 2 & 1 \\ 0 & -1 \end{bmatrix}$	(I) 6
(B) $\begin{bmatrix} 0 & 1 \\ 4 & -1 \end{bmatrix}$	(II) 5
(C) $\begin{bmatrix} 1 & 2 \\ -3 & -1 \end{bmatrix}$	(III) -4
(D) $\begin{bmatrix} 4 & -2 \\ 3 & 0 \end{bmatrix}$	(IV) -2

Choose the correct answer from the options given below:

For any invertible matrix AAA, which of the following is NOT true.

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CUET Mathematics Past Year Questions (Topic-Wise)

For any invertible matrix $A$ , which of the following is NOT true.