JEE Mathematics 2026 Question with Solution

Given:

and $B(I-A)=I+A$.

Find: The sum of the diagonal elements of $B^T B$.

From

we get

Notice that $A$ is a real skew-symmetric matrix, so

Now compute $B^T$:

Using $A^T=-A$,

Also,

so $I+A$ and $I-A$ commute.

Therefore,

Thus $B^T B$ is the identity matrix of order $3$. Hence the sum of its diagonal elements is

Therefore, the required answer is $3$.

Given: $A$ is real skew-symmetric and $B=(I+A)(I-A)^{-1}$.

Find: The sum of the diagonal elements of $B^T B$.

For a real skew-symmetric matrix, the Cayley transform

is an orthogonal matrix. Hence

Since the identity matrix is of order $3$, its diagonal sum is

Therefore, the required answer is $3$.