Matrices

Step 1: Use the inverse property.
For matrices,

Step 2: Multiply matrices and .


Step 3: Conclusion.

We have A = such that Ax=I
Since, A and I are of order 2×2. So, x will be a matrix of order 2×2
let x =
Ax = I
=
=
a + 2c = 1 ....……….(i)
4a + 3c = 0 ......……(ii)
b + 2d = 0 .....…….(iii)
4b + 3d = 1 .....…..(iv)
On solving eq (i),(ii) ,(iii) and (iv) we get
a = - , b = , c = and d = -
Substituting we get x =
∴x =

Correct Answer: Option 4

The second matrix is , which results in the equation:
A =
Now, let's perform the matrix multiplication:
[21A - 32(-32) + 32(5) 21A + 32(-3) + 32(5)] =
Simplifying:
=
[21A + 928 21A + 64] =
Equating :
21A + 928 = 10 ………… (1)
21A + 64 = 0 …………… (2)
Solving Equation 2 for A:
21A = -64
A =
Hence. Matrix A is