Question

If $A$ and $B$ are two square matrices each of order 3 with $|A| = 3$ and $|B| = 5$, then $|2AB|$ is:

• A. 30
• B. 120
• C. 15
• D. 225

Hint:

For a scalar multiple of a matrix, $|kA| = k^n |A|$ where $n$ is the order of the matrix.

Answer 1

The Correct Option is C

The determinant of a matrix $kA$, where $k$ is a scalar and $n$ is the order of the matrix, is $|kA| = k^n |A|$. For matrices $A$ and $B$, each of order 3, we have $|2AB| = 2^3 |A| |B| = 8 \times 3 \times 5 = 120$. Therefore, $|2AB| = 120$.