Which of the following are correct?

(A) For a square matrix A, if A³ = I, then A⁻¹ = A².

(B) The determinant of only a square matrix can be defined.

(C) If A is a square matrix of order 3, then the number of minors of the matrix A is 3.

(D) If A and B are two non-singular matrices of the same order, then (AB)⁻¹ = B⁻¹A⁻¹.

Choose the correct answer from the options given below:

For statement (A), given that $A^3 = I$ where $I$ is the identity matrix.

$A^3 = I$

$A \cdot A^2 = I$

By the definition of inverse matrix, if $A \cdot A^2 = I$, then $A^2$ is the inverse of $A$.

Therefore, $A^{-1} = A^2$

Statement (A) is correct.

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For statement (B), determinants are only defined for square matrices where the number of rows equals the number of columns.

A determinant can be found for a $2 \times 2$ or $3 \times 3$ matrix, but cannot be found for a $2 \times 3$ or $3 \times 2$ matrix.

Statement (B) is correct.

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For statement (C), a minor is the determinant obtained after removing one row and one column.

For a $3 \times 3$ matrix:

Number of choices for removing a row $= 3$

Number of choices for removing a column $= 3$

Total number of minors $= 3 \times 3 = 9$

Statement (C) is incorrect. The number of minors is 9, not 3.

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For statement (D), this is a standard property of matrix inverses.

To verify that $(AB)^{-1} = B^{-1}A^{-1}$:

$(AB) \cdot (B^{-1}A^{-1})$

$= A(B \cdot B^{-1})A^{-1}$

$= A \cdot I \cdot A^{-1}$

$= A \cdot A^{-1}$

$= I$

Statement (D) is correct.

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Statements (A), (B), and (D) are correct.