Question

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is INR 500.
The cost of 1 kg onion, 2 kg wheat and 3 kg rice is INR 300.
The cost of 6 kg onion, 2 kg wheat and 3 kg rice is INR 575.
The above situation can be represented in matrix form as \( AX = B \). Then \( |5A^{-1}| = \)

• A. 5
• B. 125
• C. 1
• D. 25

Hint:

When multiplying a matrix by a scalar, the determinant is multiplied by the scalar raised to the power of the matrix's order. For an \( n \times n \) matrix \( A \), \( |kA| = k^n |A| \).

Answer 1

The Correct Option is A