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Home Questions B69258HBFA
Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

Let P and Q be any two invertible matrices of the same order. Then

Match List-I with List-II

List-I Matrix

List-II Equivalent matrix

(A) $(P Q)^{-1}$

(I) $Q^{-1}P$

(B) $(P^{-1} Q)^{-1}$

(II) $QP^{-1}$

(C) $(P Q^{-1})^{-1}$

(III) $Q^{-1} P^{-1}$

(D) $(P^{-1} Q^{-1})^{-1}$

(IV) $QP$

Choose the correct answer from the options given below.

Options:

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(III), (B)-(I), (C)-(II), (D)-(IV)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

Correct Answer:

(A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Explanation:

The correct answer is Option (4) → 54

List-I Matrix

List-II Equivalent matrix

(A) $(P Q)^{-1}$

(III) $Q^{-1} P^{-1}$

(B) $(P^{-1} Q)^{-1}$

(I) $Q^{-1}P$

(C) $(P Q^{-1})^{-1}$

(II) $QP^{-1}$

(D) $(P^{-1} Q^{-1})^{-1}$

(IV) $QP$

Key identity: $(AB)^{-1}=B^{-1}A^{-1}$ and $(A^{-1})^{-1}=A$

(A) $(PQ)^{-1}=Q^{-1}P^{-1}$ → (III)

(B) $(P^{-1}Q)^{-1}=Q^{-1}(P^{-1})^{-1}=Q^{-1}P$ → (I)

(C) $(PQ^{-1})^{-1}=(Q^{-1})^{-1}P^{-1}=QP^{-1}$ → (II)

(D) $(P^{-1}Q^{-1})^{-1}=(Q^{-1})^{-1}(P^{-1})^{-1}=QP$ → (IV)

Matching: (A)–(III), (B)–(I), (C)–(II), (D)–(IV)

CUET Questions