Let be a matrix such that . If the determinant of the matrix is , then is equal to .

Question

Let  be a  matrix such that . If the determinant of the matrix  is , then  is equal to  .

Canvas Classes · Accepted Answer

🧠 Set Up the Exponent Equation, Then Solve for

Track powers of  through the nested adjugate. With  and  being :

Set equal to  and solve.

🗺️ Working It Out

Match exponents:

Expand:

So we need

Try small values of :

- : 
- : 
- : 
- :  ✓

So

⚡ The Smart Move

For "find  given a determinant equation involving nested adjugates", set up the exponent in terms of  and solve a polynomial equation. For matrices where every value is a power of a single prime (here, ), the bookkeepin

More questions from this chapter

More questions from this chapter