Statement-1 (Assertion and Statement- 2 (Reason)
Each of these questions also has four alternative
choices, only one of which is the correct answer. You
have to select the correct choice as given below.
Statement- 1 If A, B, C are matrices such that
`abs(A_(3xx3))=3, abs(B_(3xx3))= -1 and abs(C_(2xx2)) = 2, abs(2 ABC) = - 12.`
Statement - 2 For matrices A, B, C of the same order
`abs(ABC) = abs(A) abs(B) abs(C).`

Options

A. Statement- is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true, Sttatement - 2
is not a correct explanation for Stamtement-1
C. Statement 1 is true, Statement - 2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the given problem, we will analyze both statements and determine their validity step by step.

### Step 1: Analyzing Statement 1
Statement 1 asserts that if \( A, B, C \) are matrices such that:
- \( \text{abs}(A_{3 \times 3}) = 3 \)
- \( \text{abs}(B_{3 \times 3}) = -1 \)
- \( \text{abs}(C_{2 \times 2}) = 2 \)

Then, it claims that \( \text{abs}(2ABC) = -12 \).

**Step 1.1: Determinant of a Product of Matrices**
The determinant of the product of matrices can be expressed as:
\[ \text{abs}(ABC) = \text{abs}(A) \cdot \text{abs}(B) \cdot \text{abs}(C) \]
However, we must note that \( A \) and \( B \) are \( 3 \times 3 \) matrices, while \( C \) is a \( 2 \times 2 \) matrix. The multiplication of these matrices is not valid because the number of columns in \( A \) and \( B \) does not match the number of rows in \( C \).

**Conclusion for Statement 1:**
Since the multiplication of matrices of different orders is not valid, Statement 1 is **false**.

### Step 2: Analyzing Statement 2
Statement 2 states that for matrices \( A, B, C \) of the same order:
\[ \text{abs}(ABC) = \text{abs}(A) \cdot \text{abs}(B) \cdot \text{abs}(C) \]

**Step 2.1: Validity of Statement 2**
This statement is true under the condition that all matrices involved are of the same order. Since the statement specifies that \( A, B, C \) are of the same order, we can conclude that this property holds.

**Conclusion for Statement 2:**
Statement 2 is **true**.

### Final Conclusion
- Statement 1 is false.
- Statement 2 is true.

Thus, the correct choice is that Statement 1 is false, and Statement 2 is true.