Question

If $A = \begin {bmatrix} \alpha & 0 \\ 1 & 1 \end {bmatrix}$ and $B= \begin {bmatrix} 1 & 0 \\ 5 & 1 \end {bmatrix}$ then value of $\alpha$ for which $A^2=B$ is

• A. 1
• B. 2
• C. 4
• D. no real values

Answer 1

The Correct Option is D

Given, A =A = $\begin {bmatrix}
\alpha & 0 \\
1 & 1 \end {bmatrix}$ and B= $\begin {bmatrix}
1 & 0 \\
5 & 1 \end {bmatrix}$
$\Rightarrow \ \ A^2\begin {bmatrix}
\alpha & 0 \\
1 & 1 \end {bmatrix} \begin {bmatrix}
\alpha & 0 \\
1 & 1 \end {bmatrix} = \begin {bmatrix}
\alpha^2 & 0 \\
\alpha+1 & 1 \end {bmatrix}$
Also, given, A$^2$=B
$\Rightarrow \ \ \begin {bmatrix}
\alpha^2 & 0 \\
\alpha+1 & 1 \end {bmatrix} = \begin {bmatrix}
1 & 0 \\
5 & 1 \end {bmatrix}$
$\Rightarrow \ \ \alpha^2=1 \ and \ \alpha+1=5$
Which is not possible at the same time.
$\therefore $ No real values of a exists.

Answer 2

Ans. Which is not possible at the same time.  ∴ No real values of α exist.

A rectangular table or array of letters, numbers, or phrases that are organized in columns and rows is called a matrix. A matrix has a size of 2x3 or less since there are two rows and three columns.

The reason Matrix is regarded as one of the most potent tools in mathematics is that it breaks down and simplifies difficult tasks using simple approaches. Matrix has developed as a result of ongoing efforts to identify efficient and compact strategies for solving linear equation systems. The operations of the matrix's notations are used in areas of business including cost estimating, budgeting, and sales prediction. Additionally, the Matrix transcends our screen and is employed for real-world tasks like rotation, reflection, and magnification.

Square Matrix A matrix with the number of rows and columns is equal.  A m x n matrix will be square if m = n,  and it will be known as the square matrix of order ‘n’.  For example, The square matrix of 3 is: 
matrix of 3 is: 

3	-1	0
3/2	√3/2	1
4	3	-1