
If $A=\left[ \left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right) \right]$ then ${{A}^{2}}$is equal to ?
A . $\left( \begin{matrix}
8 & -5 \\
-5 & 3 \\
\end{matrix} \right)$
B. $\left( \begin{matrix}
8 & -5 \\
5 & 3 \\
\end{matrix} \right)$
C. $\left( \begin{matrix}
8 & -5 \\
-5 & -3 \\
\end{matrix} \right)$
D. $\left( \begin{matrix}
8 & 5 \\
-5 & 3 \\
\end{matrix} \right)$
Answer
162.9k+ views
Hint: We are given a question which is based on matrices. We are given a matrix and we have to find the square of that matrix. A square matrix is a matrix that has the same number of rows and columns. For example – The given matrix is $2\times 2$ matrix. To Find the square of A we multiply A to A and after simplifying it, we get the value of the square of matrix A.
Complete step by step Solution:
Given $A=\left[ \left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right) \right]$
We have to find the value of ${{A}^{2}}$
${{A}^{2}}=A\times A$
Now we put the value of A in the above equation and we get,
Then ${{A}^{2}}=\left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right)\times \left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right)$
Now we open the brackets of R.H.S and multiply the terms, we get
${{A}^{2}}=\left( \begin{matrix}
3\times 3+1\times -1 & 3\times 1+1\times 2 \\
-1\times 3+2\times -1 & -1\times 1+2\times 2 \\
\end{matrix} \right)$
Adding the terms and solving it, we get
${{A}^{2}}=\left( \begin{matrix}
9-1 & 3+2 \\
-3-2 & -1+4 \\
\end{matrix} \right)$
Simplifying further, we get
${{A}^{2}}=\left( \begin{matrix}
8 & 5 \\
-5 & 3 \\
\end{matrix} \right)$
Hence the value of ${{A}^{2}}=\left( \begin{matrix}
8 & 5 \\
-5 & 3 \\
\end{matrix} \right)$
Therefore, the correct option is (D).
Note: We know that the given question is in matrix form. A matrix is a set of numbers that are arranged in rows and columns to make a rectangular array. In the matrix, the numbers are called the entries or entities of the matrix.
In Multiplication matrices, the number of column of the first matrix match the number of rows of the second matrix. When we want to multiply the matrices, then the parts of the rows in the first matrix are multiplied by the columns in the second matrix.
Complete step by step Solution:
Given $A=\left[ \left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right) \right]$
We have to find the value of ${{A}^{2}}$
${{A}^{2}}=A\times A$
Now we put the value of A in the above equation and we get,
Then ${{A}^{2}}=\left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right)\times \left( \begin{matrix}
3 & 1 \\
-1 & 2 \\
\end{matrix} \right)$
Now we open the brackets of R.H.S and multiply the terms, we get
${{A}^{2}}=\left( \begin{matrix}
3\times 3+1\times -1 & 3\times 1+1\times 2 \\
-1\times 3+2\times -1 & -1\times 1+2\times 2 \\
\end{matrix} \right)$
Adding the terms and solving it, we get
${{A}^{2}}=\left( \begin{matrix}
9-1 & 3+2 \\
-3-2 & -1+4 \\
\end{matrix} \right)$
Simplifying further, we get
${{A}^{2}}=\left( \begin{matrix}
8 & 5 \\
-5 & 3 \\
\end{matrix} \right)$
Hence the value of ${{A}^{2}}=\left( \begin{matrix}
8 & 5 \\
-5 & 3 \\
\end{matrix} \right)$
Therefore, the correct option is (D).
Note: We know that the given question is in matrix form. A matrix is a set of numbers that are arranged in rows and columns to make a rectangular array. In the matrix, the numbers are called the entries or entities of the matrix.
In Multiplication matrices, the number of column of the first matrix match the number of rows of the second matrix. When we want to multiply the matrices, then the parts of the rows in the first matrix are multiplied by the columns in the second matrix.
Recently Updated Pages
If tan 1y tan 1x + tan 1left frac2x1 x2 right where x frac1sqrt 3 Then the value of y is

Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Verb Forms Guide: V1, V2, V3, V4, V5 Explained

1 Billion in Rupees

Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE
