JEE Mathematics 2026 Question with Solution

Given:

• $A = \begin{pmatrix} \alpha & 2 \\ 1 & 2 \end{pmatrix}$
• $B = \begin{pmatrix} 1 & 1 \\ \beta & 1 \end{pmatrix}$
• The stated matrix relation is interpreted in the solution as

Find: $(\det(\operatorname{adj}(A^3-B^3)))^2$.

The extracted solution itself states that the question is flawed and leads to a contradiction, so the published numerical answer is obtained only after assuming an intended corrected problem.

Compute the left-hand side:

Hence,

Compute the right-hand side:

So,

Equating corresponding entries gives:

and

Now check the $(2,1)$ entry:

while

Since

the given relation is inconsistent.

The published solution therefore assumes an intended corrected result:

Let

Then

For a $2 \times 2$ matrix,

Therefore,

and the required value is

So, using the assumed intended correction from the published solution, the answer is $50625$.

Given: the extracted solution explicitly notes that the original question statement is contradictory.

Find: why the answer $50625$ cannot be obtained directly from the printed relation.

The source question text has

which simplifies to

Using the displayed forms of $A$ and $B$, entrywise comparison gives incompatible values. That means there is no real pair $\alpha, \beta$ satisfying all entries simultaneously.

Because of this contradiction, the numerical result $50625$ is not derivable from the printed equation alone. The extracted solution works backward from the official answer and assumes the intended outcome was

Under that assumption,

and for a $2 \times 2$ matrix,

Hence,