NCERT Class 12-Mathematics: Exemplar Chapter –3 Matrices Part 16

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Question 44:

If and , find value of

Answer:

We have,

Also,

By using equality of matrices, we get

Which is true for all real values of .

Question 45:

If the matrix is a skew symmetric matrix, find the values of a, b and c.

Answer:

Let

Since, A is skew-symmetric matrix.

By equality of matrices, we get

Question 46:

If , then show that .

Answer:

We have,

Now,

And

Thus, we see from the eq. (i), and (ii) and (iii) that,

Hence Proved.

Question 47:

If A is square matrix such that , show that .

Answer:

Given that,

As,

I is an identity matrix.

As, I is an identity matrix.

Hence,

…proved