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P and Q are two square matrices of the same order. Which of the following statement(s) is/are correct?

1. If P and Q are invertible, then [PQ]⁻¹ = Q⁻¹P⁻¹.
2. If P and Q are invertible, then [QP]⁻¹ = P⁻¹Q⁻¹.
3. If P and Q are invertible, then [PQ]⁻¹ = P⁻¹Q⁻¹.
4. If P and Q are not invertible, then [PQ]⁻¹ = Q⁻¹P⁻¹.

Correct answer: If P and Q are invertible, then [PQ]⁻¹ = Q⁻¹P⁻¹.

Solution

The correct option states that the inverse of the product of two invertible matrices P and Q is equal to the product of their inverses in reverse order, which is a fundamental property of matrix multiplication and inverses. This means that if both matrices are invertible, the relationship holds true as stated.

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