Find the inverse of $A=\begin{bmatrix}2&1\\1&1\end{bmatrix}$ using the adjoint-determinant method, and verify that $AA^{-1}=I$.

Find the inverse of A= 21; 11 using the adjoint-determinant method, and verify that AA⁻¹=I.

Example · Example 9

A=\begin{bmatrix}2&1\\1&1\end{bmatrix}

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For $A=\begin{bmatrix}2&1\1&1\end{bmatrix}$ , $\det A=2(1)-1(1)=1$ . Since $\det A eq0$ , $A$ is invertible, and $A^{-1}=\dfrac{1}{\det A}\begin{bmatrix}1&-1\-1&2\end{bmatrix}=\begin{bmatrix}1&-1\-1&2\end{bmatrix}$ (diagonal entries swapped, off-diagonal entries negated, divided by $1$ ). Verifying $AA^{-1}$ : position $(1,1)$ : $2(1)+1(-1)=1$ ; position $(1,2)$ : $2(-1)+1(2)=0$ ; position $(2,1)$ : $1(1)+1(-1)=0$ ; po …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set ANNUAL1 markMCQ
$Q. Matrices A and B will be inverse of each other only if$
(a) AB = BA
(b) AB = BA = O
(c) AB = O, BA = I
(d) AB = BA = I
›Reveal solutionSolution

Two square matrices are inverses of each other exactly when both products give the identity matrix.

By definition, if $A$ and $B$ are square matrices of the same order such that $AB=BA=I$ (the identity matrix), then $B$ is called the inverse of $A$ (written $B=A^{-1}$ ) and $A$ is the inverse of $B$ . A si …

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CBSE 2025Set ANNUAL1 markMCQ
$Q. If the matrix (4 -k; -2 3) has no inverse matrix, then the value of k is$
(a) 6
(b) -6
(c) 12
(d) -12
›Reveal solutionSolution

A matrix has no inverse exactly when its determinant is zero.

A square matrix is invertible only if it is non-singular, i.e. $\det\ne 0$ . "No inverse matrix" means the matrix IS singular, so we need $\det = 0$ .

…

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CBSE 2024Set ANNUAL1 markMCQ
$A$
(a) $AB=BA$
(b) $AB=BA=0$
(c) $AB=0, BA=I$
(d) $AB=BA=I$
›Reveal solutionSolution

By definition, A and B are inverses of each other exactly when their product (in either order) gives the identity matrix.

A square matrix $B$ is the inverse of $A$ if $AB=BA=I$ , where $I$ is the identity matrix of the same order. This is the standard definition of ma …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. Matrices A and B will be inverse of each other only if-$
(a) $AB = BA$
(b) $AB = BA = 0$
(c) $AB = 0, BA = I$
(d) $AB = BA = I$
›Reveal solutionSolution

Inverse of a matrix is defined by the identity relation on both sides.

By definition, if $A$ is a square matrix and there exists a matrix $B$ of the same order such that $AB=BA=I$ (the identity matrix), then $B$ is called the inverse of $A$ (written $B=A^{-1}$ ), and $A$ is the i …

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Q.Find the inverse of $A=\begin{bmatrix}2&1\\1&1\end{bmatrix}$ using the adjoint-determinant method, and verify that $AA^{-1}=I$ .

Concept understanding — Invertible Matrices and Uniqueness of Inverse

Q.Find the inverse of A=[2111]A=\begin{bmatrix}2&1\\1&1\end{bmatrix}A=[21​11​] using the adjoint-determinant method, and verify that AA−1=IAA^{-1}=IAA−1=I.

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Q.Find the inverse of $A=\begin{bmatrix}2&1\\1&1\end{bmatrix}$ using the adjoint-determinant method, and verify that $AA^{-1}=I$ .

Unlock everything free for 14 days